kde_capone.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kernel Density Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kernel density estimation is a popular approach for estimating the underlying probability distribution of data in terms of the probability density function. The probability density function gives us the relative likelihood of different observations, and is a very useful tool in data analyis and exploration. For example, the density function can tell us whether the data is unimodal, bimodal, skewed, etc. The densities can be used as features in models. A common application is anomaly detection where the density function is used to determine how likely a new observation is relative to others. \n",
    "\n",
    "To understand density estimation in general, and kernel density estimation in particular, let us start with a dataset that contains the credit card transactions over the last six months for a single customer. There are 100 elements in the dataset and each element corresponds to the dollar amount of a credit card transaction. The data is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "amounts  = np.array([22.38, 26.25, 21.4 , 28.72, 13.24, 25.62, 17.71, 19.89, 22.7 ,\n",
    "       19.56, 25.5 , 14.09, 13.62, 22.35, 17.43, 15.72,  9.73, 22.4 ,\n",
    "       25.51, 19.76, 21.08, 26.96, 22.84, 15.49, 18.47, 27.23, 18.06,\n",
    "       25.82, 25.4 , 19.86, 21.82, 22.17, 26.66, 20.1 , 26.02, 19.76,\n",
    "       17.77, 27.74, 19.64, 14.66, 23.32, 18.95, 21.08, 20.88, 22.34,\n",
    "       26.28, 21.79, 22.  , 18.93, 15.33, 11.33, 19.03, 19.31, 15.56,\n",
    "       20.87, 15.26, 16.52, 18.47, 27.1 , 25.48, 11.55, 27.84, 11.03,\n",
    "       20.2 , 17.37, 23.37, 18.8 , 16.95, 28.47, 16.76, 21.63, 17.85,\n",
    "       17.16, 18.2 , 20.  , 22.02, 16.32, 15.34,  7.56, 21.77, 18.84,\n",
    "       13.05, 26.12, 25.49, 16.29, 13.95, 22.61, 22.64, 11.08, 22.17,\n",
    "       19.75, 21.57, 23.7 , 22.01, 19.84, 15.02, 14.65, 20.95, 20.69,\n",
    "       16.94])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way to summarize the above information is to create a histogram. In the code that follows, we first create 5 bins  that cover different ranges of dollar amounts (\\$5 to \\$9,99, \\$10 to \\$14.99, etc.), and then use the \"hist\" function to both count the number of transactions that fall into each bin and plot the histogram. The height of each bin in the histogram corresponds to the number of elements in that bin (these numbers are also conveniently returned by the hist function as shown in the output below). For example, there are two elements in the first bin (\\$5 to \\$9.99), 11 elements in the next (\\$10 to \\$14.99), 37 elements in the third bin, and so on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2., 11., 37., 31., 19.]),\n",
       " array([ 5, 10, 15, 20, 25, 30]),\n",
       " <a list of 5 Patch objects>)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a histogram\n",
    "bins = np.arange(5, 31, 5) # This produces the array [ 5, 10, 15, 20, 25, 30]. \n",
    "plt.hist(amounts, bins = bins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, if we normalize the histogram such that the area under the histogram is 1, then we get a rough estimate of the probability density of the data (we discuss the probability density function in a little bit more detail below). To do this, we first divide the height of each bin by the total number of points in the entire dataset (100, in our example) and then divide the resulting number further by the width of each bin (5, in our case). The hist function does this for us automatically if we set the parameter \"density\" to True. This is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probaility Density')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(amounts, bins = bins, density=True)\n",
    "plt.xlabel(\"Amount in dollars\")\n",
    "plt.ylabel(\"Probaility Density\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability density function gives us the relative likelihood of different observations. For example, the density that we estimated above tell us that it is about 3 times more likely for a transaction amount to lie in the interval \\[20, 25) than the interval \\[10, 15). We can use this information for anomaly detection: for example, a transaction amount of \\$60 is very unlikely compared to an amount in the range, say, [15, 20] and so it is likely to be a fraudalant transaction (assuming that the 100 transactions in our dataset are representative of the user's purchasing behaviour)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The histogram provides a rough estimate of the density that is piece-wise constant. What if we want a smoother estimate? Well, we could fit a Gaussian to our data - that would work as long as the underlying density can be modeled with a Gaussian. How do we fit a Gaussian? A Gaussian has two parameters (mean and standard deviation) and we can estimate them as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean =  19.985100000000003\n",
      "std dev =  4.545832045951543\n"
     ]
    }
   ],
   "source": [
    "amount_mean = np.mean(amounts)\n",
    "amount_stddev = np.std(amounts)\n",
    "print(\"mean = \", amount_mean)\n",
    "print(\"std dev = \", amount_stddev)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having estimated the parameters of the Gaussian, we can create a of plot the density using the \"stats\" module from \"scipy\". To do that, we first instantiate a Gaussian with the mean and standard deviation calculated above. Next, we generate 100 values on the x-axis, compute the densities at those points using the Gaussian, and plot those values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probaility Density')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "# Instantiate the Gaussian\n",
    "G = stats.norm(loc=amount_mean, scale=amount_stddev)\n",
    "\n",
    "# Generate 100 points along the x-axis on either side of the mean \n",
    "xx = np.linspace(amount_mean-4*amount_stddev, amount_mean+4*amount_stddev, 100) \n",
    "\n",
    "# Compute the densities at those 100 points\n",
    "yy = G.pdf(xx) \n",
    "\n",
    "# Plot\n",
    "plt.plot(xx, yy, c='r', label=\"G\")\n",
    "plt.xlabel(\"Amount in dollars\")\n",
    "plt.ylabel(\"Probaility Density\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can overlay the Gaussian on the histogram as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probaility Density')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(amounts, bins = bins, density=True)\n",
    "plt.plot(xx, yy, c='r', label=\"G\")\n",
    "plt.xlabel(\"Amount in dollars\")\n",
    "plt.ylabel(\"Probaility Density\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above approach to generating a smooth estimate of the density works as long as the underlying data can be modeled by a single Gaussian. But, what if the data is bimodal as shown by the histogram below? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.002, 0.01 , 0.04 , 0.03 , 0.018, 0.   , 0.   , 0.008, 0.032,\n",
       "        0.052, 0.008]),\n",
       " array([ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60]),\n",
       " <a list of 11 Patch objects>)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "amounts2 = np.array([19.89, 22.34, 28.61, 23.03, 20.24, 18.43, 24.69, 26.54, 21.71,\n",
    "       19.37, 22.08, 14.7 , 17.78, 25.24, 23.77, 18.87, 24.74, 16.86,\n",
    "       23.33, 26.66, 23.15, 18.16, 19.79, 11.85, 19.06, 18.84, 22.89,\n",
    "        9.07, 13.67, 17.36, 22.5 , 25.44, 12.68, 17.29, 25.79, 25.1 ,\n",
    "       19.82, 16.18, 27.22, 21.67, 19.41, 22.18, 15.82, 16.07, 14.97,\n",
    "       19.39, 16.76, 19.5 , 29.54, 23.48, 43.18, 51.7 , 47.72, 45.43,\n",
    "       51.93, 42.88, 48.86, 47.01, 47.28, 49.33, 46.59, 46.55, 53.62,\n",
    "       49.17, 51.52, 48.69, 53.51, 50.52, 45.78, 47.66, 44.11, 49.69,\n",
    "       50.2 , 52.9 , 51.2 , 51.42, 50.48, 52.47, 53.27, 53.68, 49.41,\n",
    "       52.13, 51.16, 54.65, 50.29, 50.97, 55.9 , 45.01, 49.62, 57.09,\n",
    "       55.51, 50.23, 51.13, 44.93, 51.87, 56.45, 53.77, 50.85, 50.49,\n",
    "       52.51])\n",
    "plt.hist(amounts2, bins = np.arange(5, 61, 5), density=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above data is bimodal and a single Gaussian would not be a good fit. However, it looks like we can get a decent estimate of the density by fitting a mixture of two Gaussians, a technique that is covered in Chapter 9 - Gaussian Mixture Models. But what if we do not know the number of modes in our data or, worse, if the data cannot be modeled as a mixture of Gaussians? Kernel density estimation (KDE) is a technique that will produce a smooth density estimate irrespective of the underlying distribution. Depending the kernel used (more about this later), we get different estimates for the same data. An estimate for the above data using the Gaussian kernel is shown below in Figure 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we learn how KDE works, let us revisit the histogram based approach and look at how we can make the histogram a little bit smoother. In other words, we want to see how can we lessen the abrupt changes in the height of the histogram as we move from one bin to the next. This will lead us directly to KDE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us consider a very simple dataset of 5 numbers: x = \\[8, 6, 7, 21, 22]. A histogram of this data using the bins [5,10), [10,15), [15,20) and [20,25] is shown below in Figure 2(a) where the 5 observations (i.e., data points) are plotted as little colored dots. For the purpose of this discussion, let us assume that each observation contributes a block of height 1 to the bin in which it lies as shown on Figure 2 (b). For example, there are three observations in the first bin, each contributing a block, and hence the height of the first bin is 3. Similalry there are two observations in the last bin, each contributing a block and so height of the last bin is 2. Note that we are working with the unnormalized histogram - we can easily normalize it to get an estimate of the probability density.\n",
    "\n",
    "\n",
    "The above histogram has abrupt changes in height as we move from one bin to the next. We can lessen these changes by getting rid of the bins altogether, and have each observation contribute a block centered horizontally around that observation. This is shown in Figure 3. For example, the red dot, located at $amount~=~6$, contributes a block of the same height and width as before (height = 1, width = 5), but that block is centered horizontally at $amount~=~6$, i.e., it extends horizontally from 3.5 to 8.5. Similarly, the blue dot contributes a block centered horizontally at $amount~=~7$, and so on.\n",
    "\n",
    "Now, to compute the $unnormalized$ density at any arbitrary point on the x-axis, we just sum up the heights of the blocks that cover that point. This is shown in Figure 4. For example, to compute the density at x = 5, we sum up the heights of the blocks that cover x=5 in Figure 3; there are two blocks that cover x=5, and hence the unnormalized density at x=5 is estimated as 2. Similalry, 3 blocks cover x=8 and hence the unnormalized density at x=8 is 3. No blocks cover x=15 and so the unnormalized density there is 0. Clearly, this estimate looks better than the histogram-based estimate. It captures the fact that the observations are spaced apart and it does not have the abrupt changes caused by binning (or, at least, those changes are not as severe).\n",
    "\n",
    "Finally, to obtain an estimate of the probability density, we simply normalize the height so that the area under the curve is 1. The normalized version is shown in Figure 5. We will soon learn about generating such plots using scikit-learn.\n",
    "\n",
    "\n",
    "What we just saw is an example of kernel density estimation. The box is referred to as the kernel. Instead of a box-shaped kernel, we could try kernels of other shapes. The Gaussian kernel is a popular choice and it produces smoother estimates. An estimate based on the Gaussian kernel is shown below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kernel density estimation using the Gaussian kernal works exatly the same way as the estimation using the box kernel: we place a Gaussian kernel centered at each observation and just sum up the values of those Gaussians (and normalize). An example is shown in Figure 6. There are 5 observations and so we have 5 Gaussians, each centered around an observation. To compute the unnormalized density at, say, $amount=25$, we add the values of the 5 Gaussians at that position. The left three Gaussians are practically zero at $amount=25$, the teal Gaussian has a value of 0.044, and the megenta Gaussian has a value of 0.078. Summing those values, we get an unnormalized estimate of 0.122 for the density at $amount=25$.\n",
    "\n",
    "\n",
    "So far, we conveniently left out an important aspect of kernel density estimation: the kernel size. For the box kernel, we used a box of width of 5, and for the Gaussian kernel we used a Gaussian with a standard deviation of 2.5. As you might expect, different values for the kernel size would produce different estimates. When the kernel size is large, each observation exerts its influence over a larger region and vice versa. Figure 7 shows the density estimate for the same dataset with a narrow Gaussian kernel (standard deviation = 0.2) and Figure 8 shows the density estimate with a wide kernel (standard deviation = 5). As you can see, the wider the kernel, the smoother the estimate.\n",
    "\n",
    "\n",
    "How do we detemine the kernel size? One approach is to leave out a small portion of the data as a validation set and perform KDE on the remaining data for different values of kernel size. Then we compute the likelyhood of the validation data for each of those estimates and choose the kernel size that produces the largest likelyhood. In scikit-learn, you can do this using \"GridSearchCV\".\n",
    "\n",
    "We turn to the scikit-learn implementation of KDE next."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kernel Density Estimation in SKLearn\n",
    "\n",
    "In this section, we look at KDE in scikit-learn. Let us start with the import first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KernelDensity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us work with the \"amounts2\" data that we saw earlier. Let us call it \"x\" for convenience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([19.89, 22.34, 28.61, 23.03, 20.24, 18.43, 24.69, 26.54, 21.71,\n",
       "       19.37, 22.08, 14.7 , 17.78, 25.24, 23.77, 18.87, 24.74, 16.86,\n",
       "       23.33, 26.66, 23.15, 18.16, 19.79, 11.85, 19.06, 18.84, 22.89,\n",
       "        9.07, 13.67, 17.36, 22.5 , 25.44, 12.68, 17.29, 25.79, 25.1 ,\n",
       "       19.82, 16.18, 27.22, 21.67, 19.41, 22.18, 15.82, 16.07, 14.97,\n",
       "       19.39, 16.76, 19.5 , 29.54, 23.48, 43.18, 51.7 , 47.72, 45.43,\n",
       "       51.93, 42.88, 48.86, 47.01, 47.28, 49.33, 46.59, 46.55, 53.62,\n",
       "       49.17, 51.52, 48.69, 53.51, 50.52, 45.78, 47.66, 44.11, 49.69,\n",
       "       50.2 , 52.9 , 51.2 , 51.42, 50.48, 52.47, 53.27, 53.68, 49.41,\n",
       "       52.13, 51.16, 54.65, 50.29, 50.97, 55.9 , 45.01, 49.62, 57.09,\n",
       "       55.51, 50.23, 51.13, 44.93, 51.87, 56.45, 53.77, 50.85, 50.49,\n",
       "       52.51])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = amounts2\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the histogram again for easy reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.002, 0.01 , 0.04 , 0.03 , 0.018, 0.   , 0.   , 0.008, 0.032,\n",
       "        0.052, 0.008]),\n",
       " array([ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60]),\n",
       " <a list of 11 Patch objects>)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(amounts2, bins = np.arange(5, 61, 5), density=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computing a kernel density estimate is as simple as instantiating a \"KernelDensity\" object and calling its \"fit\" method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KernelDensity(algorithm='auto', atol=0, bandwidth=5, breadth_first=True,\n",
       "              kernel='gaussian', leaf_size=40, metric='euclidean',\n",
       "              metric_params=None, rtol=0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Instantiate\n",
    "kde = KernelDensity(kernel='gaussian', bandwidth=5)\n",
    "\n",
    "# Fit. We need to reshape the 1-D array x into 2-D first\n",
    "kde.fit(x.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first parameter specifies the type of kernel we want and the second parameter specifies its size (see below). There are 6 available kernels in sklearn - their names and shapes are shown in Figure 9. The box kernel is referred to as the top-hat kernel in sklearn and you would specify it as \"tophat\".\n",
    "\n",
    "The bandwidth parameter specifies the half-width for the tophat kernel, the standard deviation for the Gaussian kernel and so on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having fit the model to the data, we can calculate the density at specific points using the \"score_samples\" which returns the logarithm of the densities. We show this in the next few cells where we compute the log-densities at the points 20, 22 and 29.\n",
    "\n",
    "**Note**: In what follows, we use the terms _density_ and _likelihood_ interchangeably."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20],\n",
       "       [22],\n",
       "       [29]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let us evaluate the densities at three points 20, 22 and 29.\n",
    "# Start by creating an containing those points\n",
    "test_samples = np.array([20, 22, 29]).reshape(-1,1)\n",
    "test_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.52280412, -3.53836157, -4.29079525])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the score_samples function to get the log-densities\n",
    "log_densities = kde.score_samples(test_samples)\n",
    "log_densities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02951655, 0.0290609 , 0.01369403])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# If you want the densities instead of the log-densities, \n",
    "# compute the exponent of the values returned by score_samples\n",
    "densities = np.exp(log_densities)\n",
    "densities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that the log-likelihood of a dataset is just the sum of the log-likelihoods of the individual data points. You can compute the log-likelihood of a dataset using the \"score\" method as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-11.351960935170196"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kde.score(test_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can confirm that the above output is the same as the sum of the individual likelihoods as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-11.351960935170196"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(log_densities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do we create a plot of the density estimate? It is easy. We just generate a range of x-values, compute the densities at those values and use matplotlib's plot function. This is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20f22ea2888>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iWSISDNwHbB+xz3acjbwAHwZ2G2OMiMQArwJfM8a8O7SziASKSILrdhDwQeDU+F6KmiilDV0U13Zw95IZVocyqruXplLRfInjVe1Wh+K3+uyDFF5oudzA6ummR4eRGR9OQbmOBxhuzATgquk/BuwEioEXjDFFIvKEiNzl2u1pIF5ESoEvAUNdRR8DsoFvjOjuGQLsFJETwDGgGvjZRL4wdf12nKxFBO5YON3qUEa1ZUEKwYEBbNfGYMucqGqnd8Dh8Q3Aw63KiudgeQsObQe4zK2ZvYwxO4AdI7Z9c9jtXuDeUY77DvCdK5x2ufthqqm042Qt+RmxHtu1Lyo0iJtzEnj9VC3f+OA8jxyB6uv2n29GhClbG2IirMiK4/nCSkobu5jjgdNWWEFHAqv3KW3ooqSu02O//Q/ZsmA6Ne29WgayyP7zzcxLiSIm3PPr/0NWZMYCcKhCy0BDNAGo99lxshaA2xd4dgLYPC+ZwADhtVO1Vofid3oHBjly0fP7/4+UHhdOYmQIh7Qd4DJNAOp9hso/KdGeWf4ZEh0exI3ZCbx+qk57A02xY5Vt9NkdXtH/fzgRYUVmLIcqWq0OxWNoAlCXnW/0jvLPkNsXpHCh+RLFtZ1Wh+JX9p9vJkCcNXVvsyIzjuq2HmraeqwOxSNoAlCX7TjhKv8sTLE4EvfcmpdMgMDrWgaaUgfKmpk/I5rosCCrQ7lmK1zTmhRe0KsA0ASghnn1ZC3LM2KZHh1mdShuiY8IYWVWHDtO6RoBU6XPPsjRyjav6v0z3NyUSKYF2yjUhmBAE4ByqWjqpqSuk9sXeMe3/yG3L5hOaUMXpQ1aBpoKxyvb6bc7WOmlCSDQFsCyDG0HGKIJQAHw5ul6AG6b710JYCje107qVcBUOOiaUtlbEwBAfkYcJXUdtPcMWB2K5TQBKMA59/+86VGkxYVbHco1SYkOZUlaDG8V11sdil8oKHfO/+NN/f9HWpEZizFw5KJeBWgCUDR19VF4odXyZR+v1+a8ZI5XtVPf0Wt1KD5tYNDB4QutXlv/H7IkPYbAANF2ADQBKGB3cQPGOD9IvdEt85xx7yrWReUm06nqdi71D3rF9M9XEx4cyPzUaG0HQBOAwln+SY0JY/6MKKtDuS5zkiNIiwvTMtAkG5pJc4WHrBA3HisyYjlW2Ua/3WF1KJbSBODnLvXb2Xuuic15yV47qZqIcMu8ZPaVNnGp3251OD7rYHkLsxOnkRjp/au6Ls+Ipd/u4FSNf88lpQnAz/3lbBN9dofX1v+HbJ6XTL/dwd5zTVaH4pMGHYZD5S2szPLu8s+Q5a6J4Y74+YAwTQB+7o3TdUSHBXnlsP7hVmTFERkayFuntQw0GYprO+jss7N6lne/T4YkRYaSHhdOoZ+3A2gC8GP2QQe7SxrYNDeJIJt3vxWCbAFsyE1id0mDLvw9CYbq/97c/3+k5RmxFF5o9evJBL37r16NS+GFVtouDXCLl5d/htySl0xzdz/HKv37W91kOFjeTHpcuNdME+KO5RmxNHX1UdnivxPDaQLwY7tLGgiyCWtzEqwOZUKsm5NIYIDw5mntDjqRjDEcLG/xid4/wy3PcLYDFF7w3/EAmgD82FvF9ayeFU9kqPfN6jia6LAgVmbFsbtE2wEmUmlDF62XBljlI/X/IXOSI4kMCeSwHzcEawLwU+VN3ZQ1drNpbpLVoUyoDblJnK3voqr1ktWh+Iyh+r+3jwAeyRYgLEmP0QSg/M8u16CpTfN8o/4/ZIMroe0502hxJL7jYHkLyVEhpHvZPFHuyM+I40x9Jx29/jkxnFsJQES2iMgZESkVkcdHeTxERJ53PV4gIpmu7ZtF5LCInHT93jjsmOWu7aUi8kPx1lFIXmp3SYNrBK1v/VHPTpxGelw4e0q0HWAiDNX/V2bFe+1AwatZnuGcGO7oxTarQ7HEmAlARGzAj4HbgTzgfhHJG7HbI0CrMSYbeBL4rmt7E3CnMWYh8DDw3LBj/gt4FMhx/WwZx+tQ16Cjd4CD5S1snOtb3/7BOSp449wk3jvfRO/AoNXheL3Klh7qOnp9qvvncEvSYwgQOOynE8O5cwWwEig1xpQZY/qBbcDWEftsBZ5x3X4J2CQiYow5aoypcW0vAkJdVwvTgShjzH7j7IT7LHD3uF+NcstfzjZidxhumedb9f8h63MT6R1wsL+s2epQvF6Ba/5/X6v/D4kICWRuShSH/XRqaHcSQCpQOex+lWvbqPsYY+xAOzByzPiHgKPGmD7X/lVjnBMAEXlURApFpLCxUeu6E2FXcQOx4UEsTY+1OpRJsXpWPGFBNi0DTYCD5S3EhgeRnRhhdSiTJj8zlqMX27AP+t/EcO4kgNEKfyOHzl11HxGZj7Ms9KlrOKdzozFPGWPyjTH5iYmJboSrrmbQYdhzpoENuUnYAnyvpgsQGmRjTXY8u0sa/HqU50Q4WOHs/x/go+8VcLYDXOofpKTO/5YVdScBVAFpw+7PBGqutI+IBALRQIvr/kzgj8BDxpjzw/afOcY51SQ4etE5+nejj5Z/hmyYm0RVaw+lDV1Wh+K16tp7udB8yWfr/0OGBoT5Y3dQdxLAISBHRLJEJBi4D9g+Yp/tOBt5AT4M7DbGGBGJAV4FvmaMeXdoZ2NMLdApIqtdvX8eAl4Z52tRbthV0kBggHDzHN++mtqQ60xwu7UMdN0OVgz1//eNGUCvJDUmjJSoUAo1Afw1V03/MWAnUAy8YIwpEpEnROQu125PA/EiUgp8CRjqKvoYkA18Q0SOuX6Gvnp+Bvg5UAqcB16bqBelrmxPSQP5mbFE+cjo3yuZERPG3JRI9pzRBHC9DpY3ExESyLzpkVaHMqlEhOUZsX45NXSgOzsZY3YAO0Zs++aw273AvaMc9x3gO1c4ZyGw4FqCVeNT3dZDSV0n/3THXKtDmRLrc5P4+d4yOnsHfGa6i6lUUNbC8oxYAr18plh3LM+I5dWTtdS29/jUhHdj8f3/WXXZUK+YjT42/cOVbMhNxO4wvFuqi8Rcq+auPs41dPnc/D9Xkp/pn+0AmgD8yJ6SBtLjwpntw136hluWEUtkSCB7SrT78LU66KPz/1zJvOlRhAXZ/G6BGE0AfqJ3YJB3zzexcW6STw7pH02QLYC1cxJ4+6x2B71WBeUthAYFsDA1xupQpkSQLYDFadF6BaB80/7zzfQOOC5PluYv1ucmUd/RR3Gt//XxHo+Ccmf9PzjQfz4i8jPiOF3bwaV+u9WhTBn/+d/1c7tLGggLsvnNJf2Q9a7urm+f1d5A7mq/NEBJXYfPd/8caXlGLIMOw7FK/5kYThOAHzDGsLukgTXZCYQG2awOZ0olRYUyf0YUb2s7gNsOVrRgjP/U/4csc02NctiP2gE0AfiBcw1dVLf1sMnHR/9eyfrcRA5fbKW9xz/nfL9WBWXNBAcGsDjNP+r/Q6LDg5iTHOFXE8NpAvADQ6Nhh0bH+psNuUkMOgz7zml3UHccrGhhaVqM310tApcHhDkc/tFpQBOAH9hd3EDe9ChSokOtDsUSS9JiiAoN1FHBbujsHeBUdbvflX+GLM+Io6PXzjk/mUNKE4CPa780wOGLrX5b/gEItAVw85xE3jnb6Dff7K5X4YVWHAZWzfKvBuAhK1wDwgov+McCMZoAfNw75xoZdBi/6/450obcJBo7+zhd22F1KB6toKyFIJtcbhD1N+lx4SRGhvjNgDBNAD5ud3E9cdOCWTzTvxr0RlqX6+oOqmWgqyoob2bRzBjCgv2v/g/OieFWZMZyyE+WiNQE4MMGHYZ3zjayfk6izy7+4q6EiBAWz4xmzxntDnol3X12Tlb5b/1/SH5GHFWtPdS291gdyqTTBODDjlW20uoHi7+4a11uEkcvttLa3W91KB7pUEULdofhhtn+Wf8fsiLTmQD9oQykCcCH7SpuwBYgrM3x7cVf3LUhNxGHgb+c06uA0ewvaybIJuRn+PcVwLzpkYQH2yj0gzKQJgAftrukgfyMWKLDdC58gEUzY4ibFsw7WgYa1YHzzSxNi/Xb+v+QQFsAy9JjOaRXAMpb1bgWf/Hn7p8j2QKEdXMSeVu7g/6Vjt4BTla3s9rPyz9D8jNjKanroKPXt0ePawLwUbv9bPEXd63PTaSlu58T1e1Wh+JRDpa14DBwg5/2/x9pRWYcDgNHL/r2xHCaAHzUruJ6MuL9Z/EXd92ck0iA/PfqaMppv2v+n6Xp/t1deMiStBhsAeLz7QCaAHzQpX47755vZtPcZL9Z/MVdsdOCWZIWo+MBRth/vpn8jFi/nP9nNNNCApk/I8rnxwNoAvBB+8410W93aP3/CjbOTeJ4VTuNnX1Wh+IRWrv7Ka7r0PLPCPkZcRyrbKPf7rA6lEnjVgIQkS0ickZESkXk8VEeDxGR512PF4hIpmt7vIjsEZEuEfnRiGPedp3zmOtHP60myK7iBiJDAi/3Z1bvNzQthl4FOBWUN2MMft//f6QVmbH0Djg4VeO77UVjJgARsQE/Bm4H8oD7RSRvxG6PAK3GmGzgSeC7ru29wDeAf7zC6R8wxixx/ehf4wRwOAy7Shq4OTfRr5bzuxZ506NIiQq93FDu7/afbyYsyMYiP58uZKR81xeog+W+WwZy5xNiJVBqjCkzxvQD24CtI/bZCjzjuv0SsElExBjTbYzZhzMRqClworqdpq4+btHyzxWJCBvmJrHXVSrzd/vLmsnP9K/1f92RGBnC7MRpFJQ1Wx3KpHHnfzwVqBx2v8q1bdR9jDF2oB1w53ryl67yzzfkCq2VIvKoiBSKSGFjow7gGcuu4noCBNbP0QRwNRvnJtHVZ/f5Rr6xNHT2cra+ixtnJ1gdikdaNSuewopWBn103Ig7CWC0D+aR/xru7DPSA8aYhcBa18+Do+1kjHnKGJNvjMlPTNQpDcbyVnED+RlxxE4LtjoUj7YmO57gwAB2Fft3GejdUucqaWtzNAGMZlVWHJ19dk7X+OY04u4kgCogbdj9mUDNlfYRkUAgGrjqVytjTLXrdyfwW5ylJjUONW09FNd2aO8fN4QHB3LDrHi/XyVs37lmYsODyJseZXUoHmm1q2dUQblvloHcSQCHgBwRyRKRYOA+YPuIfbYDD7tufxjYbYy54hWAiASKSILrdhDwQeDUtQav3m9XcT0Am+YlWxyJd9g0L4nypm7KGv1j+b+RjDHsK23kxuwEAvx8uvArSY4KJTM+nANlvlkqDBxrB2OMXUQeA3YCNuAXxpgiEXkCKDTGbAeeBp4TkVKc3/zvGzpeRCqAKCBYRO4GbgUuADtdH/424C3gZxP6yvzQG6frmZUwjdmJ06wOxStsyE0Cithd0sAsPxwxXdrQRX1HH2uztfxzNSuz4thZVI/DYXwuUY6ZAACMMTuAHSO2fXPY7V7g3iscm3mF0y53L0Tljo7eAQ6UNfOJNVk6+tdNaXHhzEmOYHdJA59cO8vqcKbc3nPO+v9NWv+/qlVZ8bxQWMWZ+k7m+VipTPt9+Yi3zzQyMGi4db6Wf67FxrnJHCxvob3Ht2d9HM2+0iayEqYxMzbc6lA82qpZzvEAvtgdVBOAj3ijqI6EiBCWpPnnYt7Xa3NeEnbX0pn+pN/u4EBZM2uydfTvWGbGhpMaE0aBDw4I0wTgA/rsg7x9ppFb5iX5/dq/12pJWizx04J583S91aFMqaMXW7nUP8hN2dq12h2rZsVxsLyFq/Rt8UqaAHzAgbIWuvrsWv65DrYAYdO8JN4uafCrUcHvljYRIDr/j7tWZ8XT3N1PaYNv9RjTBOAD3iiqIzzYpqM5r9PmvBQ6++w+29d7NHtLm1icFqPLhbppqB1gv4+1A2gC8HIOh+HN0/Wsm5Ooc7lfp5uyEwgNCuAtPykDtV8a4HhlGzdp90+3pcc52wGGRk77Ck0AXu5EdTsNnX1a/hmHsGAbN2Un8ubpep+r8Y5mb2kjDuNcHlO5R0RYkx3P/vPNPjUvkCYAL7ezqA5bgLgGNanrdWteMjXtvRT56Jwvw+0paSQmPEh7jF2jNdkJdPTaKfKh9QE0AXgxYwyvnazlxtnxxITr5G/jsXFeEiLwVrFvl4EcDsM7Zxu4OSdRe4xdo6E2tndLfacdQBOAFyuu7aSi+RK3L0my+skAABikSURBVJhudSheLyEihOXpsT7fHfRkdTtNXf1snKtXjNcqMTKE3ORI3jvvO+0AmgC82GunagkQtP4/QTbnJVNU00FlyyWrQ5k0e840IAI3z9H6//W4MTueQxUt9NkHrQ5lQmgC8FLGGF49WcuqrHgSIkKsDscnbFmQAjjbVXzVnjONLEmLIU7Xi7gua2Yn0Dvg4MiFNqtDmRCaALzUuYYuyhq7uWNhitWh+IyM+GnMnxHFjpO1VocyKZq6+jhR1cZG7TBw3VbNisMWID5TBtIE4KV2nKxFBG6brwlgIt2+IIUjF9uobe+xOpQJ986ZRoyBDVr/v26RoUEsmhntM+MBNAF4qddO1rEiI46kqFCrQ/Epty90Nqi/fsr3ykB7zjSQGBmiq3+N05rZCRyvaqez1/tnkNUE4IVKG7o4U9/J7Vr+mXCzEyPITY7kNR9LAPZBB38528iG3ESfW9Rkqt2YHc+gw1DgA6uEaQLwQq+5atRDjZZqYm1ZkMKhihYaOnutDmXCHKpopaPXrgMGJ8DyjFjCg20+MYW4JgAvY4xh+/Ea8jNimR4dZnU4PumOhdMxBnYW+c6YgJ1FdYQEBrBOp38Yt5BAGzfOjuftsw1eP3WIJgAvU1LXybmGLrYumWF1KD5rTnIEsxKn8fop3+gNZIxhZ1EdN89JJDzYrVVg1RjW5SZR2dJDWVO31aGMiyYAL/PKsRpsAcIdC3X072QREW5fkML+8800dfVZHc64nahqp7a9ly3aY2zCrHcNpHv7jHeXgTQBeBGHw/Cn4zWszUkgXgd/Tao7F8/AYeDVE95/FfB6UR2BroVv1MRIiwtnduI03j7TYHUo4+JWAhCRLSJyRkRKReTxUR4PEZHnXY8XiEima3u8iOwRkS4R+dGIY5aLyEnXMT8UEe2aMIYjF1upbuvR8s8UmJsSxdyUSF4+Vm11KONijGHnqTpWz9IJAyfa+twkCspb6On33mkhxkwAImIDfgzcDuQB94tI3ojdHgFajTHZwJPAd13be4FvAP84yqn/C3gUyHH9bLmeF+BPXjlWQ2hQAJvz9FJ+KmxdksrRi21caPbeOm9pQxdlTd3cpj3GJtz63ET67Q72l3nvoDB3rgBWAqXGmDJjTD+wDdg6Yp+twDOu2y8Bm0REjDHdxph9OBPBZSIyHYgyxuw3zmb0Z4G7x/NCfN3AoINXT9Zyy7xkIkK0IW8q3OW60tp+rMbiSK7f66fqnCPG83TCwIm2MiuOsCCbV7cDuJMAUoHKYferXNtG3ccYYwfagautNp3qOs/VzgmAiDwqIoUiUtjY6L3/0OO1r7SJlu5+7lqs5Z+pkhoTxsqsOF4+Vu213f12nq5jWXqsjhifBJe7g55p9Nr3hzsJYLTa/MhX684+17W/MeYpY0y+MSY/MdF/+zC/crSaqNBA7cc9xe5eksr5xm6vXCmssuUSp6o7uE2nC58063MTudhyiXIv7Q7qTgKoAtKG3Z8JjLwmvryPiAQC0cDVxklXuc5ztXMql47eAV47Vcedi2cQEqgLv0+lOxamEGQTXj7qfY3B2487/6R0waDJs941snp3iXf2BnInARwCckQkS0SCgfuA7SP22Q487Lr9YWC3uco1kTGmFugUkdWu3j8PAa9cc/R+4s/Ha+mzO7g3P23sndWEigkPZt2cJLYfr/GqxcCNMfzxaDUrMmNJiwu3OhyflRYXTm5yJG946UpyYyYAV03/MWAnUAy8YIwpEpEnROQu125PA/EiUgp8CbjcVVREKoDvA38nIlXDehB9Bvg5UAqcB16bmJfke148XMmc5AgWz4y2OhS/dM/SVBo6+9jnRVMAF9V0UNrQxd1LR21aUxPotvnJFFa00OyFgwbd6k5ijNkB7Bix7ZvDbvcC917h2MwrbC8EFrgbqL8qbejk6MU2vn7HPHSohDVuyUsiNjyIbQcvss5LllJ8+Wg1QTbhAzpifNLdOj+FH+4u5a3iej6yIt3qcK6JjgT2cC8WVmELEP0mZ6GQQBsfWjaTN0/X09jp+d/yBh2GV47XsCE3SQd/TYH5M6JIjQnzyskDNQF4MPuggz8crWZDbhKJkTr1g5XuW5mG3WH4/ZGqsXe22Hvnm2js7OMe/dIwJUSE2+ansO9cE119dqvDuSaaADzYO2cbaezs42/zZ469s5pU2UmRrMiM5flDlR7f5/uPR6uJDA3UpR+n0G3zk+kfdPCOlw0K0wTgwZ4/VElCRLD+IXuI+1akU97UzQEPXgnqUr+dnafq+MDC6YQGaZfhqZKfGUfctGB2FnnXSnKaADxUbXsPbxXX86HlMwmy6X+TJ7hj4XQiQwPZduii1aFc0Wsn6+juH2TrEi3/TCVbgHDLvCT2lDTQb3dYHY7b9JPFQ/224CIG+NiqDKtDUS5hwTbuWZrKa6fqaO3utzqcUf264AKzEqexelac1aH4ndvmp9DZZ+e9897TXVgTgAfqtzv43cFKNuYm6SAeD/PRVenO/x8PvAo4Vd3O0YttfGxVhnYZtsCa7AQiQgK9ag0JTQAe6PWiOpq6+njwBv3272nmpkRxU3YCz7xX4XGX+s/tv0BYkI0PLddOA1YIDbJx2/wUXj9VR++Ad6wRoAnAAz23v4KM+HBuzvGOQUf+5pNrs6jv6ONPxz1n+qr2SwO8cryau5fOIDosyOpw/NbdS2fQ2Wf3mrmBNAF4mOLaDg5VtPKxVRkEBOhlvCdaNyeR3ORIfra3zGO6hL50pIreAQcfW61XjVa6cXYCiZEhXjN5oCYAD/PcgQuEBAZwr/b991giwiNrsyip6/SI+YEcDsOvD1xgWXoM82fofFFWsgUIdy2ewdtnGmm75JkdBYbTBOBBmrv6+MORKu5ZmqpD+D3c1iUzSIwM4Wd7y60OhX2lTZQ3dfPQDZlWh6JwriHRP+hgx0nPHxOgCcCDPPNeBX12B//j5llWh6LGEBJo4+EbMvjL2UaKa61dLOZHe0pJjgrh9oW67q8nWJAaxezEabx8zPPLQJoAPER3n51n9l9g87xkZidGWB2OcsPHVmcQGRLI9988a1kM+883c7C8hc+sm62LBXkIEeHuJakcLG+huq3H6nCuShOAh3j+UCXtPQN8at1sq0NRbooJD+ZT62bx5ul6Dl9otSSG/9h1lqTIEO5b6V3TEPu6oZHYr3j4VYAmAA8wMOjg6X3lrMyMY3lGrNXhqGvw8TVZJESE8O+vl0x5j6CCsmYOlLXw6XWzdd4fD5MeH87KrDieP1SJw4NXktME4AH+dLyG6rYePrVOa//eZlpIIP9zYzYF5S385dzU9gj6j13nSIgI4aOr9Nu/J3pgVToXmi+x1wN6il2JJgCLORyG//vOeeYkR7AhV2f99Eb3r0xnZmwY//56yZR92ztY3sJ755v59LpZ+u3fQ21ZkEL8tGB+feCC1aFckSYAi/3pRA1n67v43IZsHfjlpYIDA/iHW+dQVNMxJT0/7IMOvr29iOSoEB7QyQI9Vkigjb9dkcau4npqPLQxWBOAhQYGHTz55lnmpkRy56IZVoejxuGuxaksSYvhn/98mqZJXhz82f0XOF3bwbfunE9YsH7792QfXZmOAbYdqrQ6lFFpArDQ7w9XUdF8iX+4NVe//Xs5W4DwvQ8vortvkG9tL5q056lr7+X/vHGG9bmJ3L5A+/17urS4cNbNSWTbwYsMDHrW5IHgZgIQkS0ickZESkXk8VEeDxGR512PF4hI5rDHvubafkZEbhu2vUJETorIMREpnIgX40367IP8cNc5lqTFcMs8rf37gpzkSD6/KZtXT9Ty+qnJGQX6xJ+LsDsMT9y1QKd89hIfW5VBQ2cfb532vEXjx0wAImIDfgzcDuQB94tI3ojdHgFajTHZwJPAd13H5gH3AfOBLcBPXOcbssEYs8QYkz/uV+JlfltwkZr2Xr58W67+IfuQT62bTd70KL7xyqkJnwvmrdP17DhZx+c35ZAer+tEeIsNc5NIjQnjF+9aP23ISO5cAawESo0xZcaYfmAbsHXEPluBZ1y3XwI2ifNTbSuwzRjTZ4wpB0pd5/NrHb0D/HhPKTfMimdNdoLV4agJFGQL4Hv3LqK1u58vPn8M+wRd9pc1dvGlF44xNyWS/7FWuwt7E1uA8MhNWRyqaOVguWetJ+1OAkgFhrdgVLm2jbqPMcYOtAPxYxxrgDdE5LCIPHrtoXuvH7x5jubufv7pjnlWh6ImwfwZ0TyxdQFvn2nk238qGvcAsY7eAT75bCGBtgB+9lA+wYHadOdt7l+ZTty0YH7ydqnVobyPO++k0eoTI9/RV9rnaseuMcYsw1la+pyI3Dzqk4s8KiKFIlLY2NjoRrie7Wx9J8/sr+D+leksnKlT9/qqj65K59PrZvPrAxf5+ThmDB10GP7nb49ysfkSP3lgmS4R6qXCgm08clMWb59p5FR1u9XhXOZOAqgC0obdnwmMXArp8j4iEghEAy1XO9YYM/S7AfgjVygNGWOeMsbkG2PyExO9e4UsYwzfeqWIiJBAvnxrrtXhqEn2ldty+cCi6fzLjmJeuI5ugH32Qb76+xO8c7aR/711PqtnxU9ClGqqPHiDc/JAT7oKcCcBHAJyRCRLRIJxNupuH7HPduBh1+0PA7uN87p3O3Cfq5dQFpADHBSRaSISCSAi04BbgVPjfzme7dWTtewva+Yfb51D7DSd79/XBQQI/+fexazJjucrvz/B1/94kj67e2vFNnT28tGfFfDS4Sq+sClHB3z5gKjQIB66MYPXTtVR2tBldTiAGwnAVdN/DNgJFAMvGGOKROQJEbnLtdvTQLyIlAJfAh53HVsEvACcBl4HPmeMGQSSgX0ichw4CLxqjHl9Yl+aZ+nsHeBfXi0mb3oUH9U/Zr8RGmTjmY+v5FM3z+I3BRf52/+7/6p//MYY9p1r4q7/fJfTNR38+KPL+PvNc6YwYjWZPrEmi5DAAH6yxzOuAsRT1jR1R35+viks9M4hA1996QQvHq7kpc/cyLJ0nfHTH71+qpZ/fPEEXX12VmbFcd+KNJakxeAwzlr/u6VN/KbgAucbu0mNCeOph5brEo8+6F93FPPU3jL+9NhNLEidmv9fETk8Wnd7TQBTYHdJPZ/4VSGfWT+br26Za3U4ykINnb28dLiKFw5VUtF86a8eX5IWwwOr0rlz8Qyd5M1HdfQOsP57b5OTFMG2R1dPyTigKyWAwEl/Zj/X2t3PV39/krkpkXzxlhyrw1EWS4oM5bPrs/nMutkUXmilpq0HESFAYFZCBHkzoqwOUU2yqNAg/n7zHL7x8il2FtWzxcIpPTQBTLJvbS+itbufX318hS7Zpy4TEVZkxlkdhrLI/SvSeG5/Bf/6WjEb5iZa9tmgI0om0e8OXmT78Rq+sClHa7lKqcsCbQH8rw/kcaH5Es+8V2FZHJoAJsnRi61865Uibp6TyGc3ZFsdjlLKw9w8J5GNc5P4wVvnuNDcbUkMmgAmQWNnH5/59RGSo0P44X1LsOlUz0qpUXzn7gXYAoQvv3iCQQvWDtYEMMEGBh089tsjtPX089OP5RMTrgO+lFKjmxETxrfvnM/BihZ+sW/qZwvVBDCBHA7DP7xwnILyFv7tbxZpjw6l1Jj+Zlkqt+Yl8703znC2vnNKn1sTwAQxxvCt7UVsP17DV7fM5e6lIydMVUqpvyYi/H9/s5DIkEC+uO0YPf3uTRcyETQBTJDvv3mW5w5c4FPrZvGZ9bOtDkcp5UUSIkL4/+9dTHFdB//w4jEcU9QeoAlgnIwxfG9nCf+5u5T7VqTxuI70VUpdhw1zk/j6HfPYcbKOJ986OyXPqQPBxsE+6ODrfzzF84WV3L8yne/creu0KqWu3yM3ZXGuvov/3F3K7MSISS8lawK4Tj39g3x+21HePF3P5zdm8/eb5+iHv1JqXESEf757ARXN3Xz5peOEBtkmdaoILQFdh9KGLu7+8bu8VVzPE1vn86VbdWF3pdTECA4M4KmH8lmQGs3nfnuEV45VT9pzaQK4Rq8cq+auH+2jsauPZz6+koduyLQ6JKWUj4kOC+K5R1aRnxHLF58/dl0ryrlDE4CbGjv7+PzvjvKFbceYPyOKHZ9fy81zvHuJSqWU54oICeRXH1/JTdkJfP3lk1S1/vX04eOlbQBjcDgMzxdW8q87iukdcPDFW3L43IZsgmyaO5VSkyss2MbPH87n2MU2ZsaGT/j5NQFcgTGGN0/X8+Rb5yiu7WBVVhz/cs9CspMirA5NKeVHQgJtrJoVPynn1gQwgn3QwVvF9fzk7fOcqGonMz6cH3xkCVuXzNCGXqWUT9EE4FLd1sNLhVX87uBF6jp6mRkbxr9/aBF/syyVQC33KKV8kN8mAGMMFc2XePN0HTtO1nGssg2AdXMS+c7dC9gwN0mncVZK+TS/SQD2QQfnG7s5XtXGwfIW3ittoqa9F4AFqVF8ZUsuH1w4g/T4iW9oUUopT+RWAhCRLcB/ADbg58aYfxvxeAjwLLAcaAY+YoypcD32NeARYBD4vDFmpzvnnEiP/OoQ751vpmfAOcteTHgQN86O57OzE7g5J1E/9JVSfmnMBCAiNuDHwGagCjgkItuNMaeH7fYI0GqMyRaR+4DvAh8RkTzgPmA+MAN4S0TmuI4Z65wTJiN+Gunx4SyeGcPCmdFkxU8jQMs7Sik/584VwEqg1BhTBiAi24CtwPAP663At123XwJ+JM4uM1uBbcaYPqBcREpd58ONc06Yb96ZNxmnVUopr+ZO95ZUYPg45CrXtlH3McbYgXYg/irHunNOAETkUREpFJHCxsZGN8JVSinlDncSwGi1kpGrFVxpn2vd/tcbjXnKGJNvjMlPTNSpF5RSaqK4kwCqgLRh92cCNVfaR0QCgWig5SrHunNOpZRSk8idBHAIyBGRLBEJxtmou33EPtuBh123PwzsNsYY1/b7RCRERLKAHOCgm+dUSik1icZsBDbG2EXkMWAnzi6bvzDGFInIE0ChMWY78DTwnKuRtwXnBzqu/V7A2bhrBz5njBkEGO2cE//ylFJKXYk4v6h7h/z8fFNYWGh1GEop5VVE5LAxJn/kdp3kRiml/JQmAKWU8lNeVQISkUbgwnUengA0TWA4U0ljn3reGjdo7Fbx5NgzjDF/1Y/eqxLAeIhI4Wg1MG+gsU89b40bNHareGPsWgJSSik/pQlAKaX8lD8lgKesDmAcNPap561xg8ZuFa+L3W/aAJRSSr2fP10BKKWUGkYTgFJK+SmfTwAiskVEzohIqYg8bnU8YxGRX4hIg4icGrYtTkTeFJFzrt+xVsY4GhFJE5E9IlIsIkUi8gXXdm+IPVREDorIcVfs/9u1PUtEClyxP++auNDjiIhNRI6KyJ9d970ibgARqRCRkyJyTEQKXdu84T0TIyIviUiJ6z1/gzfEPZJPJ4Bhy1neDuQB97uWqfRkvwK2jNj2OLDLGJMD7HLd9zR24B+MMfOA1cDnXP/W3hB7H7DRGLMYWAJsEZHVOJc2fdIVeyvOpU890ReA4mH3vSXuIRuMMUuG9aH3hvfMfwCvG2PmAotx/vt7Q9zvZ4zx2R/gBmDnsPtfA75mdVxuxJ0JnBp2/www3XV7OnDG6hjdeA2v4Fzz2atiB8KBI8AqnKM6A0d7L3nKD861NHYBG4E/41xsyePjHhZ/BZAwYptHv2eAKKAcVycab4l7tB+fvgLgGpae9HDJxphaANfvJIvjuSoRyQSWAgV4SeyuMsoxoAF4EzgPtBnnEqfgue+dHwBfARyu+/F4R9xDDPCGiBwWkUdd2zz9PTMLaAR+6Sq9/VxEpuH5cf8VX08Abi89qSaGiEQAvwe+aIzpsDoedxljBo0xS3B+o14JzBttt6mN6upE5INAgzHm8PDNo+zqUXGPsMYYswxnmfZzInKz1QG5IRBYBvyXMWYp0I03lHtG4esJwFeWnqwXkekArt8NFsczKhEJwvnh/xtjzB9cm70i9iHGmDbgbZztGDGuJU7BM987a4C7RKQC2IazDPQDPD/uy4wxNa7fDcAfcSZfT3/PVAFVxpgC1/2XcCYET4/7r/h6AvCVpSeHL7n5MM76ukcREcG5MlyxMeb7wx7yhtgTRSTGdTsMuAVno94enEucggfGboz5mjFmpjEmE+d7e7cx5gE8PO4hIjJNRCKHbgO3Aqfw8PeMMaYOqBSRXNemTThXPfTouEdldSPEFDTY3AGcxVnT/brV8bgR7++AWmAA5zeNR3DWdXcB51y/46yOc5S4b8JZajgBHHP93OElsS8CjrpiPwV807V9Fs41rEuBF4EQq2O9ymtYD/zZm+J2xXnc9VM09PfpJe+ZJUCh6z3zMhDrDXGP/NGpIJRSyk/5eglIKaXUFWgCUEopP6UJQCml/JQmAKWU8lOaAJRSyk9pAlBKKT+lCUAppfzU/wOFYYkqsiPK6wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Our data values lie in the range [9.07, 57.09]. i.e., x.min() = 9.07 and x.max() = 57.09\n",
    "# Let create a plot that covers the range [0, 65]\n",
    "# Generate 100 evenly spaced points in the range [0, 65]\n",
    "xx = np.linspace(0, 65, 100)\n",
    "\n",
    "# Let us compute the densities at those 100 points. Note the use of np.exp to convert log-densities to densities\n",
    "yy = np.exp(kde.score_samples(xx.reshape(-1,1)))\n",
    "\n",
    "# Plot\n",
    "plt.plot(xx, yy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the process with a smaller bandwidth. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20f22f0f8c8>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kde = KernelDensity(kernel='gaussian', bandwidth=1)\n",
    "kde.fit(x.reshape(-1, 1))\n",
    "\n",
    "# Plot\n",
    "xx = np.linspace(0, 65, 100)\n",
    "yy = np.exp(kde.score_samples(xx.reshape(-1,1)))\n",
    "plt.plot(xx, yy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1\n",
    "\n",
    "Try running the above code with different values of bandwidth and different kernels. You can find the kernel names in Figure 9."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing the right bandwidth using GridSearch\n",
    "\n",
    "As we just saw, different values for the bandwidth parameter produce different density estimates. How to we find the right bandwidth? One approach is to split the data into a \"training\" set and a \"validation\" set (we use the term \"training\" eventhough there is no training in the traditional sense), perform KDE on the training set for different values of bandwidth and evaluate the resulting estimates on the validation set. The bandwidth that maximizes the log likelyhood of the validation set (recall the \"score\" method discussed earlier) can be chosen as the best bandwidth to use. Scikit-Learn provides GridSearchCV which uses [cross-validation](http://scikit-learn.org/stable/modules/cross_validation.html) to pick the best value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code segment shows how to use GridSearchCV. There are four steps to this process - the comments in the code explain each step in detail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'bandwidth': 3}\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "# STEP 1:\n",
    "# Create a dictionary of key-value pairs. The keys are the parameters to optimize and\n",
    "# the value corresponding to each key is a list that contains the parameter values to search over. \n",
    "# The following dictionary has one key ('bandwidth') and the corresponding value is the list [1, 2, 3, ..., 10].\n",
    "# GridSearchCV will try all those values for the bandwidth and pick the best one.\n",
    "# If you also want to find the best value for another parameter, say, kernel, look at the example in the next cell.\n",
    "param_dict = {'bandwidth': np.arange(1, 11, 1)}\n",
    "\n",
    "# STEP 2:\n",
    "# Instantiate GridSearchCV.\n",
    "# The first parameter specifies the model whose parameters we are trying to optimize.\n",
    "# The second parameter is a dictionary as described above\n",
    "# The third parameter specifies the number of folds to use during cross validation (if you do not know what this means, please refer to the \"cross-validation\" reference above)\n",
    "gridsearch = GridSearchCV(KernelDensity(kernel='gaussian'), param_dict, cv=5); \n",
    "\n",
    "# STEP 3:\n",
    "# Let gridsearch search over the parameter values you specified.\n",
    "gridsearch.fit(x.reshape(-1, 1))\n",
    "\n",
    "# STEP 4:\n",
    "# Print out the best values for the parameters.\n",
    "print(gridsearch.best_params_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above output shows that the best value for bandwidth (among those we specified) is 3. \n",
    "\n",
    "The next cell shows how to search for two parameters (\"bandwidth\" and \"kernel\") at the same time. Note that \"param_dict\" now has two keys, and the first parameter to GridSearchCV is now \"KernelDensity( )\" instead of \"KernelDensity(kernel='gaussian')\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'bandwidth': 3, 'kernel': 'gaussian'}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:788: RuntimeWarning: invalid value encountered in subtract\n",
      "  array_means[:, np.newaxis]) ** 2,\n"
     ]
    }
   ],
   "source": [
    "# STEP 1:\n",
    "# Create a dictionary of key-value pairs. The keys are the parameters to optimize and\n",
    "# the value corresponding to each key is a list that contains the parameter values to search over. \n",
    "# The following dictionary has two keys: 'bandwidth' and 'kernel'. \n",
    "# The value for the first key is the list [1, 2, 3, ..., 10].\n",
    "# The value for the second key is the list ['gaussian', 'tophat', 'epanechnikov']\n",
    "# GridSearchCV will try the specified values for bandwidth and kernel.\n",
    "\n",
    "param_dict = {'bandwidth': np.arange(1, 11, 1), 'kernel': ['gaussian', 'tophat', 'epanechnikov']}\n",
    "\n",
    "# STEP 2:\n",
    "# Instantiate GridSearchCV.\n",
    "# The first parameter specifies the model whose parameters we are trying to optimize.\n",
    "# The second parameter is a dictionary as described above\n",
    "# The third parameter specifies the number of folds to use during cross validation (if you do not know what this means, please refer to the \"cross-validation\" reference above)\n",
    "gridsearch = GridSearchCV(KernelDensity(), param_dict, cv=5); \n",
    "\n",
    "# STEP 3:\n",
    "# Let gridsearch search over the parameter values you specified.\n",
    "gridsearch.fit(x.reshape(-1, 1))\n",
    "\n",
    "# STEP 4:\n",
    "# Print out the best values for the parameters.\n",
    "print(gridsearch.best_params_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above output shows that the best option for 'kernel' (among the three values we specified) is 'gaussian' and the best value for bandwidth (among the 10 values we specified) is 3.\n",
    "\n",
    "Let us fit a KDE with those parameter values and plot the density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20f22f73308>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xHhU50mK5FG8SfQdQOOt+ATB3yHXxGHcNPhkYnH2A1roemADWzj2B1vr7WustWustmZmZ3kcvfMLh1Lzd2MeuigwsFmPWLfG4dV0uo1N2DrYOLn2wCLg6d31+vYFLH8yVmRBNSlwkjbIJyYK8SfSHgHKl1AqlVBRwH7B3zjF7gU+4b98NvKa11u7viQBQShUDq4CzPolc+MyJzhGGJme4vsL4D9lryzKIjrDwSn2P0aGIeZzoMHZp4vko5VrzpklaLBe0ZKJ319QfAl4E6oFntNYnlVJfUUrd6T7sR0C6UqoJeBjwtGBeCxxXSh0DfgV8Smvd7+u/hFie/Q19KOVKskaLjbJyXXkGL5/qkS6KIFTbOUJBaiyp8b7fjGY5yrISaeiVzpuFeNXqqLXeB+yb89gXZ92eAu6Z5/t+Cvx0mTEKP9vf0Me6/GTSE4Kji2J3VTav1PdyunuMSgPnDMSlTnSMBEX//FzlWQk8OTnDwISNjCB5HwcTuTI2zI1cmOFo+zC7yo0v23jcsDobpeCVU1K+CSYjkzO0DU4GxdIHc3nWvGmU8s28JNGHuXeb+nE4NdevCp5En5kYzcbCFKnTBxmjtw5cTHmWq8VSVkCdnyT6MLe/sY/E6Ag2FgbXKO2mymyOd4zQMzpldCjCrbZzGAjORJ+dFE1idIR03ixAEn0Y01rz5pk+rinLINIaXG+F3VXZADKqDyInOkYoTo8jOS7S6FAuoZSiLDtBSjcLCK6fbhFQzX3jnB+ZYlcQtFXOVZ6VQFFanNTpg0ite4/YYCXbCi5MEn0Ye6vR1el6XbnxbZVzKaW4qTKbd5oHmJiWVTOMNjhho3P4QlB23HiUZyXSP25jUHabuoQk+jD2bvMARWlxFKYFbpORy3HD6ixsdicHWmSRM6MF24qV8ylzd940SZ3+EpLow5TDqaluGeDq0nSjQ1nQlpJUYiIt7G+Q9Y+MdqLDNREbzIm+PMvdYinlm0tIog9Tp86PMjplZ2cQJ/qYSCs7VqZfLDEJ49R2jLAyI56kmOCbiPXIS44lLsoqE7LzkEQfpt5tdiXPnSuDN9ED7CrPpKV/gvbBSaNDCWvBtjTxfCwW95o3Urq5hCT6MPVeywBlWQlkJV2yanRQ2VXhmije3yjlG6P0jU3TNTIV1B03HmVZiVK6mYck+jA043BysHUw6EfzAKWZCeQlx/BWg5RvjFLrrs8H09LECynPTqBndJqRCzNGhxJUJNGHodqOESZtjqCeiPVQSrGrIpN3mvuxO2QzEiMcbx/GomBtfvAvMOeZkJXyzftJog9D77nr8ztCYEQPcF15JmNTdo61DxsdSlg63jFCRXYicVFeLXZrKFnzZn6S6MPQu80DVOYmBd2a4gu5tiwDi4L90n0TcFprajuGg/pCqdkKUmOJibTQIJ037yOJPsxMzTg4fG4oJMo2HslxkWwoTJF+egN0DF1gaHImJOrz4Oq8Kc1MkP1j55BEH2aOtg0zbXeGxETsbLvKM6ntGGZ4Ui5vD6Tj7onYDSGS6AEqshOll34OSfRh5kDLABYF21amGR3KZbmuPAOnhveaZTmEQKrtGCHKamFVTqLRoXitPDuB7tEp6byZRRJ9mDnQMsCavOSgvsJxPhsKU4iLsvKuJPqAOt4+TGVeElERoZMqKmRC9hKh878nlm1qxsHR9mG2rwit0TxApNXCthVpF6/oFf7ncGrqOkfYECITsR4V2a5ELxOy/00SfRg53j6Mze5ke4jV5z2uLk2nuW9Cdp0KkJa+cSZsjpCZiPUoSI0lNtIqE7KzSKIPI9WtgygF20pCb0QPcHWpazkEGdUHhue6hVAb0VssirIs2W1qNkn0YeRAywCVOUlBuRWcN6pyk0iOjeTdJqnTB0JtxwjxUVZWZiYYHcplK8+WFsvZJNGHCZvdyZG2IbaHWLfNbBaLYufKdN5tHkBrbXQ4plfbMcza/GSsFmV0KJetIjuR3rFpRial8wYk0YeN2o5hpmacbF8RmvV5j2vK0ukcvkCbLFvsVza7k/quMTYUhlZ93qPCvdtUg3TeAJLow0Z16yBASHbczLbzYp1eyjf+VN81is3hDKkLpWbzrHkj5RsXSfRh4kDLAKtzEkNmfZuFlGbGk5UYLYnez462DQFwVVFoJvr8FNltajZJ9GFgxuHk8LmhkB/Ng2vZ4mvKMnivuV/q9H50rH2Y7KRocpODe2OahXh2m5IRvYsk+jBwotO1/nyo9s/PtbM0nf5xm1wQ40dH24fZWJiCUqE3EetRnp1Io6xLD0iiDwvVLa76/DYTjOjhv/e5fU/66f1icMLGuYFJripKNTqUZanITqBvbFoWwkMSfViobh2gPCuBjIRoo0PxicK0OApSYzng/gATvnWs3VWf3xiiHTce5bIUwkWS6E3O7nByqHUwpPvn57NjZTrVrQM4nVKn97Vjba6tA0NhM/DFeLYVlDq9JHrTO3l+lAmbI2S2DfTWjpXpDE3OSJ+0HxxtH2ZVThLx0cG/deBi8lNiiY+SNW9AEr3pHWhxtSGapT7vscP9G8oBabP0KadTc8w9ERvqlFJU5CRyplsSvSR6kzvQMuDuPQ/NNrmFFKTGUZgWy3stkuh9qaV/nLEpe8j2z8+1OieJ091jYd+KK4nexOwOJzVnh0zTVjnXjhXpVLcOSp3eh462uVasvMoEI3qAytxERi7M0B3mS1t7leiVUnuUUmeUUk1KqUfmeT5aKfW0+/lqpVSJ+/HdSqnDSqkT7j9v8G34YjGnukYZm7abrj7vsWNlOsOTM5yRGqzPHG0fJjE6gtIQXLFyPqtzkgA43RXe75ElE71Sygo8DtwCVAH3K6Wq5hz2ADCktS4DHgO+5n68H7hDa70O+ATwU18FLpbm6Z/fYbL6vMeOUtcH2AEp3/jMsbZhNhSmYAnBFSvn49nr9nSY1+m9GdFvA5q01i1aaxvwFHDXnGPuAn7ivv0scKNSSmmtj2qtz7sfPwnEKKXM0cwdAg60DLAyI56sJHPV5z3yU2IpSouTDcN9ZNJm53T3qGnq8wDJsZHkJcdwunvU6FAM5U2izwfaZ93vcD827zFaazswAsytF3wYOKq1np57AqXUg0qpGqVUTV9fn7exi0U4nJqDZ83XPz/XjpVpUqf3kePtIzh16F8oNdfq3CQp3XhxzHy/w839qVr0GKXUGlzlnE/OdwKt9fe11lu01lsyMzO9CEkspb5rlLEp89bnPXasTGfkwkzY/2ruC0fcK1ZuLg7tpQ/mWp2TSHPfODa70+hQDONNou8ACmfdLwDOL3SMUioCSAYG3fcLgF8BH9daNy83YOEdT9061DcaWYrng0zaLJev5uwgZVkJpMSF9lLWc63OTcLu1DT3he9SCN4k+kNAuVJqhVIqCrgP2DvnmL24JlsB7gZe01prpVQK8DzwqNb6HV8FLZZ2oGWAkvQ4ckJ0mVlv5aXEUpweJxOyy+R0ag6fG2KLyUbzAJUXJ2TDt06/ZKJ319wfAl4E6oFntNYnlVJfUUrd6T7sR0C6UqoJeBjwtGA+BJQBX1BKHXN/Zfn8byHex+5wUt0yyNVlGUaHEhA7VqRzUOr0y9LcN87olJ1NJkz0JRnxRFktYV2n92oxC631PmDfnMe+OOv2FHDPPN/3t8DfLjNGcZlOdI4wNm3n6lJzl208dpSm8XRNO/Xdo6zJC+2FuIxSc85VnzfjiD7SaqEsKyGs53HkylgT8myzt9PkE7EeF+v00mZ5xQ6fGyItPooVGfFGh+IXq3MTpXQjzOW9Ztf+sOkmWX9+KbnJsZSkx8n69Mtw+NwQm4pSQ3pHqcVU5iTRMzrN4ER4bkIiid5kpmYcHDo7yNWl4VGf9/CsT++QOv1l6x+fprV/gi0l5ivbeKzODe8JWUn0JnO0bZhpuzNs6vMeO0vTGZuyU98Vnj/Iy3HknDn752fzLIUQrksWS6I3mfea+7Eo2GbyK2Ln8lwvIG2Wl+/wuSGirJaQ31FqMZkJ0aTHR4XtQEASvcm82zzA+oIUkmIijQ4loHKSY1iRES8Tsleg5twQa/OTiIm0Gh2K3yilqMpL4pQkehHqJqbtHGsfDruyjceOla5+eqnTe2/a7uBEx4ipyzYea/KSOdM9xrTdYXQoASeJ3kQOnh3E7tRhNxHrsWNlGmPTdk6dD89R25Wo6xzB5nCyudj8pb51+cnMODSNPeG3FIIkehN5r3mAKKslLEZn8/FcN/Buc7/BkYQOT0vqVhN33HiszXdtQnKic8TgSAJPEr2J7G/oY3NxKrFR5q21LiYrKYayrISLF4yJpVW3DlKelRAW11wUpcWRGBMhiV6Ert7RKU53j7GrIryXeb66NJ1DZwfDeklab9kdTg6HwZ4FHkop1uYlc1ISvQhV+xtd5YpdFeFZn/e4ujSDSZuD4x3DRocS9OrOjzJhc5h+KevZ1hUkU989xowjvAYCkuhN4s2GPjISoql0b4YcrnasTEMpeLdJyjdLqfbsWRAmI3qAtfnJ2OxOGsJsQ3lJ9CbgcGrebuxjV0WGaTZ1vlIpcVGszUvmHZmQXVJ166BrT+FEc+9ZMNvaPNdA6GRneHVmSaI3gbrOEYYmZ7g+zOvzHleXpnO0bYgLtvDrl/aWw6k51Bo+9XmPkvR4EqLDb0JWEr0J7G/oQym4Nkw2GlnK1WUZzDg0h87KapYLqe8aZWzaHlb1eQCLxXWFbN15SfQixOxv7GNtXnJYtMh5Y2tJKpFWJW2Wi6hudX0IhtuIHlwXTtV3jWIPowlZSfQhbnRqhiNtw2HfbTNbXFQEVxWmyoVTi6huGaAoLY7c5FijQwm4tflJTM04aQqjzcIl0Ye4d5tca7DvKpf6/Gw7S9M50TnCyOSM0aEEHadTc/DsINtXhN9oHri4SmddGE3ISqIPcfsb+0iIjjDlps7LcU1ZBlrDgVYp38zV0DvG8OQM28Nkq8m5VmQkEBdlpS6MJmQl0YcwrTWv1fdyTVk6kVb5r5xtY2EKcVFW3m6U8s1cnmsMdoRhfR7AalFU5SZRG0YX1Ul2CGF1naN0j06xuyrH6FCCTlSEhR0r09nf2Gd0KEHnnaZ+StLjKEiNMzoUw1xVlEJd52jYLFksiT6EvXyqG4uCG1ZnGR1KULq+IpNzA5OcG5gwOpSgMeNwcqBlgGvLw3vyfnNxKjaHk5NhsqS1JPoQ9tKpHraUpJEWH2V0KEHJs8Db/gYZ1Xscax9mwuYI+2suNhW55rQ8++WanST6ENU+OMnp7jF2V2YbHUrQKkmPozAtljcbpE7v8Vaja0/hnSvDO9FnJcVQkBrLYUn0Ipi9Ut8DwO4qSfQLUUqxqzyT95r7Zdlit3ea+llXkEJyXHjtKTyfzcWpHGkbQmvzbz0piT5EvXyqh/KsBEoy4o0OJajtqshkwubgSFt4jNwWMzo1w7H2Ya4L87KNx+biVHpGp+kcvmB0KH4niT4EjUzOUN06KKN5L1xdmk6ERUmdHqhucW2cfo0keuC/6/ThUL6RRB+CXj/Ti8OpuUkS/ZISYyLZVJQqbZbA2419xEZa2VScYnQoQWF1TiKxkVaOtpm/n14SfQh6+VQPmYnRbCyQH1hv7KrIoK5zlP7xaaNDMdTbTf1sW5FGdER47ik8V4TVwsbCFBnRi+AzabPz2uledldlh/0mI97ytFmG81WyXSMXaO6bCPu2yrk2FadwqmuUSZvd6FD8ShJ9iHmlvpcLMw7u3JBndCghY21eMunxUbx+ptfoUAzzlvtDTurz77e5OBWHU1PbYe51byTRh5i9x86TnRTN1pLwXKfkSlgsihtWZ/H66d6w2xTa4/XTveQkxVCZm2h0KEHlqsLwmJCVRB9CRiZneLOhl9vX52GVss1luakqm9Epe1juOmWzO9nf0McNlVkoJe+b2VLjo1iZGc9Rk7ffSqIPIS+e7GbGoaVscwWuK88gKsLCK6fCr3xzsHWQCZuDG2VNpHltLU7jYKur9dSsvEr0Sqk9SqkzSqkmpdQj8zwfrZR62v18tVKqxP14ulLqdaXUuFLqO74NPfzsPX6e4vQ41hckGx1KyImLiuDasgxeru8OiyshZ3v1dA/RERauLpX6/HyuLktndMpu6vXpl0z0Sikr8NtT1cIAABPoSURBVDhwC1AF3K+Uqppz2APAkNa6DHgM+Jr78SngC8BnfRZxmOodm+Ld5n7u3JAnv35foZsqs2kfvEBDT/hsIae15tX6Xq4pyyA2Stoq5+P5AHzHxFtPejOi3wY0aa1btNY24CngrjnH3AX8xH37WeBGpZTSWk9ord/GlfDFMuyr7cKpkbLNMtxY6SpdeNYJCgfNfRO0DU7KUtaLyEyMZnVOIu80hXeizwfaZ93vcD827zFaazswAoTnPmV+svf4eVbnJFKeLV0TVyo7KYYNBcm8fCp8Ev1rp11/V0n0i7u2LINDZ4eYmjHnRiTeJPr56gRzi5zeHLPwCZR6UClVo5Sq6euTS9XnaugZ40jbML9/1dzPV3G5bqrM5lj7ML1j4fFL5qv1vVTmJpGXEmt0KEHtmrIMbHYnNWfN2X3jTaLvAApn3S8Azi90jFIqAkgGvO5j01p/X2u9RWu9JTMz09tvCxtPHmwj0qq4e3OB0aGEPM/6QK/Wm7/7ZmRyhppzQ9Jt44VtK9KIsCjeNmn5xptEfwgoV0qtUEpFAfcBe+ccsxf4hPv23cBrOtxaG/xkasbBL4908qE1OaQnRBsdTshbnZNIQWosL9R1Gx2K373R4Fr87oZKSfRLiY+OYFNRqmnr9EsmenfN/SHgRaAeeEZrfVIp9RWl1J3uw34EpCulmoCHgYstmEqps8A/Af+fUqpjno4dsYh9J7oYuTDDR7cXGR2KKSiluG19Lu809TM4YTM6HL96oa6bzMRoNsjid165piyDuvMjDE+a733hVR+91nqf1rpCa12qtf4792Nf1Frvdd+e0lrfo7Uu01pv01q3zPreEq11mtY6QWtdoLU+5Z+/ijk9ebCNkvQ4dq6UuW1fuWN9Hnan5nd1XUaH4jfj067F725dmyNXUXvp2vJ0tIb3mgeMDsXn5MrYINbYM8ahs0Pcv61Ieud9aE1eEisz4/nt8blTTebxan0P03Ynt62XdlxvrS9IISE6wpR1ekn0QewJmYT1C6UUd27Io7p1kO4Rc3bfPFfbRXZSNFuKU40OJWREWi1sX5HGW439prt6WhJ9kJqYtvOLwx3cLJOwfnHHhjy0hudPmK98MzY1w5tn+rh1Xa7sWXCZPrg6i7bBSdNdPS2JPkg9daid0Sk7D1y7wuhQTKk0M4E1eUnsNWH55pX6HmwOJ7dL2eay3bwmG6UwXVeWJPogZLM7+eFbLWxbkXZxA2Phe3dsyON4+zBtA5NGh+JTzx3vIi85hqsKpdvmcmUlxrClOJUXTkqiF3629/h5ukam+LPrS40OxdRuX58LwG9rzTOqH7kww/5GKdssx4fW5FDfNcq5gQmjQ/EZSfRBxunUfO/NZlbnJPKBVXKVsD8VpMaxtSSVXxzuMM3k20vuPQtul8XvrtiH1uQA5irfSKIPMq+d7qWxd5w/vb5UWioD4N6tRbT0T3CgxRw7Tz17uIOitDg2yJ4FV6wwLY61+UmmKt9Iog8iWmv+7c1m8lNiL5YVhH/dvj6XpJgInjjYZnQoy9bcN0516yD3bi2UQcIy7VmTw9G2YdO030qiDyJvNvRRc26IT16/kgir/NcEQkyklQ9vLuCFui76x6eNDmdZnj7UjtWiuEeuu1i2PWtd5ZuXTpljVC/ZJEg4nJp/+N1pitLiuG+rrGsTSB/bXsSMQ/Ps4Q6jQ7liNruTXxzu4KbKLLKSYowOJ+SVZSVSlpXA705Iohc+9MsjHZzuHuNze1YRFSH/LYFUlpXItpI0njzYhjNEN4h++VQPAxM27tsmgwRfuWVtDtWtA3SNXDA6lGWTjBIEpmYc/ONLDWwoSOa2dVKbN8LHdhRxbmAyZPcNfepQG/kpsewql04tX7l7cwFODc8cCt3f9Dwk0QeBH7/TSvfoFI/eWimTaAbZszaH1LhIfnbgnNGhXLb2wUneauznni0FslKlDxWnx3NdeQZPH2rDEaK/6XlIojdY79gU//p6MzdVZrFDliI2THSElfu3FfHSqR6aekNrnZMnD7ZhUfCRLYVLHywuy/3bijg/MsWbDaG9I5kkeoN96TcnmXY4efTWSqNDCXsPXLuC6AgL332jyehQvDY2NcNPD5xjd1W27AvrB7ursslIiOaJ6najQ1kWSfQGeqGui9/VdfOZm8opzUwwOpywl54Qzce2F/ObY+dDZv2bnx1oY2zKzqc/WGZ0KKYUabXwkS0FvHa6J6QnZSXRG2RkcoYv/OYkVblJ/M/rVhodjnB7cNdKrBbFv77ZbHQoS5qacfCjt1u4rjyD9bJdoN/ct7Uo5CdlJdEb5O/2nWJwwsbX715PpFwcFTSyk2K4d0shzx5u5/xwcI/gnj7UTv+4TUbzflaUHndxUtbucBodzhWRDGOAF09280xNBw/uWsnafFmTJNh88vqVaA3fC+JRvc3u5HtvNrO5OJXtK9KMDsf0Pr6zhPMjU/zyaKfRoVwRSfQBdrZ/gs8+c5z1Bcl85qZyo8MR8yhIjePuzQU8cbCNlr7g7MD5zbFOzo9M8dAHy6QlNwBuqsxiXX4y33qlEZs99Eb1kugDaGrGwZ/9/AgWi+Lxj24iOsJqdEhiAX958ypiIq18ae/JoFvCeNJm57GXG1iTlyRLWQeIUoq/vLmCzuELPF0Teh04kugD6Au/rqO+a5R/vncjhWlxRocjFpGZGM1nb17FW439Qbcu+Xdea+L8yBR/c+caGc0H0PUVmWwpTuU7rzUyNeMwOpzLIok+QH6wv4X/OtzB/7qhjA+uzjI6HOGFj20voio3ia88d4pJm93ocABo6RvnB2+18Aeb8tlaIrX5QHKN6lfRMzrNz6tDa1lrSfQB8F817fzdvnpuW5fLZ26qMDoc4aUIq4Wv/t4aukam+JdXjb+ISmvNl/aeJCbCyqO3yAV2RthZms41Zel89/UmxqZmjA7Ha5Lo/ezlUz088ssTXFuWwT/du0HWIgkxm4vTuGdzAT94q4XqlgFDY3nxZDdvNfbz8M0VZCZGGxpLOPv8ntUMTdr46nOnjA7Fa5Lo/ejNhj4+/cQR1uYl8b0/2iyTryHqi3dUUZQWx0NPHqV31Jgdh7pGLvDXv65jdU4if7Sj2JAYhMv6ghT+7AOlPFPTwSuneowOxyuS6P3kV0c7eOA/DlGWmcC///E24qMjjA5JXKHEmEj+7Q83Mz5l56EnjjIT4Itmpu0OPvXzI1ywOfjOR6+S3ceCwF/cWEFlbhKP/LKWgRDYmUzeMX7ww7da+N9PH2drSRpPf3IHafFRRocklmlVTiL//x+s4+DZQb7+wumAnvurz53iaNsw37xnA2VZiQE9t5hfVISFf/rIBkYv2PnrX9cFXQvuXJLofWhqxsGjv6zlb5+v59Z1OfzHn2wlMSbS6LCEj/zeVfn80Y5ifvBWK99+tTEg53ympp2fHWjjk9ev5BbZlCaoVOYm8fDNFfyurpvvvhG8V1EDSD3BR5p6x3noiSOc7h7jUx8o5S9vXiUTryb0pTuqmJi2848vN2BzOHl4d4XfetmfqWnnkV/Uck1ZOn918yq/nEMsz4PXreR01yjfePEMCdERfOLqEqNDmpck+mVyODU/rz7HP/zuNDGRVn7yJ9u4vkKuVjSrCKuFb9yzgagIC99+rYlpu5PP71nt8w/1H+xv4e/21XNdeQb/9oebpS4fpCwWxTfu2cCEzcGX9p4kPjqCuzcXGB3WJSTRL8ORtiG++Js66jpHubYsg2/es4Gc5BijwxJ+ZrUo/v731xEdYeH7+1s41jbMP35kg0+udp6acfDNF8/ww7dbuW19Lo99ZKNsFh/kIq0Wvn3/VTzwk0N87tnjDE/aeODaFUF11bIKtkmELVu26JqaGqPDWNTp7lEef72Z3x4/T3ZSNH99WxW3r88Nqv9Y4X9aa35xpJMv7z2JU2v+721V3Lu18IpH9+829fPXv66jpX+Cj+8s5kt3rJHyXwiZmLbzv58+xkunerhxdRbfvGcDqQFsxFBKHdZab5n3OUn03nE6NdWtg/zo7VZeqe8hPsrKH+0s4aEbykiQ1smw1jE0yV/9Vy3vtQxQlBbHn1xTwj1bCr1qqfW8r35WfY7na7soTo/jq3etZZeU/0KS1pqfvHuWv993mvSEKP7PrZXcui43IB/YkuivkNaa+q4x9p3o4ldHO+kcvkBKXCR/fPUKPnF1MSlx0jYpXJxOzYsnu/nh260cPjdEYnQE21emsaUkjU1FqaQnRBEXZSXKaqFz+AItfRPUd4/yfG0XHUMXSIiO4I+vKeHTHywjJlIurAt1dZ0jPPzMMRp6xinLSuB/3VDGbety/TrXsuxEr5TaA3wLsAI/1Fr/w5zno4H/BDYDA8C9Wuuz7uceBR4AHMCfa61fXOxcRib6GYeTxp5x6jpHONAywFtN/fSNTWNRcF15Jn+wKZ+bq3KIjZIfRLGwI21DPHOonYOtg7T0Tyx4nNWiuLo0nQ9vKuBDa+R9ZTZOp2ZfXRffeqWRxt5xUuIi2V2ZzZ61OWxfme7zSsCyEr1Sygo0ALuBDuAQcL/W+tSsYz4FrNda/6lS6j7g97XW9yqlqoAngW1AHvAKUKG1XnCNT38keq01kzYH49N2xqZmGBi3MTBho398ms6hC5wbmOTc4CTNvePY3Fc9psVHcW1ZBteVZ3D9qkyyEmWSVVy+/vFpajuGGZuyM2lzMD3jICc5ltLMeIrS42RZjDDgdGpePd3LvhNdvFLfw9iUHaVgRUY86/KTKc1MIC8llvyUWEoy4shNjr2i8yyW6L35SNkGNGmtW9wv9hRwFzB7RZ+7gL9x334W+I5yzUzeBTyltZ4GWpVSTe7Xe+9K/iKLqe8a5aEnjmB3auwOzYzDic3hZGrGwbTdyUKfZ1ERFgpTYylKc+0LuTY/mbV5SZSkx2ORiTCxTBkJ0dywOtvoMISBLBbF7qpsdldlY7M7OdAywLH2YWo7RjjYOshvjp2/eOxt63J5/GObfB6DN4k+H5i9pUoHsH2hY7TWdqXUCJDufvzAnO/Nn3sCpdSDwIMARUVF3sb+PnFRVlblJBJhsRBhVURaLMREWoiOtBIdYSE+OoLEmAgSoiNIj48mPSGK9IQoMuKjJaELIQIiKsLCrorM9022T8046B6ZonP4gt/WxPLmVefLgnPHxwsd4833orX+PvB9cJVuvIjpEsXp8Xz3Y5uv5FuFEMIwMZFWSjLiKcmI99s5vJkC7gAKZ90vAM4vdIxSKgJIBga9/F4hhBB+5E2iPwSUK6VWKKWigPuAvXOO2Qt8wn37buA17Zrl3Qvcp5SKVkqtAMqBg74JXQghhDeWLN24a+4PAS/iaq/8sdb6pFLqK0CN1nov8CPgp+7J1kFcHwa4j3sG18StHfj0Yh03QgghfE8umBJCCBNYrL1SVksSQgiTk0QvhBAmJ4leCCFMThK9EEKYXNBNxiql+oBzy3iJDKDfR+EEUqjGDRK7UST2wAvmuIu11vOubx10iX65lFI1C808B7NQjRskdqNI7IEXqnFL6UYIIUxOEr0QQpicGRP9940O4AqFatwgsRtFYg+8kIzbdDV6IYQQ72fGEb0QQohZJNELIYTJmSbRK6X2KKXOKKWalFKPGB3PYpRSP1ZK9Sql6mY9lqaUelkp1ej+M9XIGBeilCpUSr2ulKpXSp1USv2F+/Ggj18pFaOUOqiUOu6O/cvux1copardsT/tXo476CilrEqpo0qp59z3QyXus0qpE0qpY0qpGvdjQf9+AVBKpSilnlVKnXa/53eGSuyzmSLRuzcwfxy4BagC7ndvTB6s/gPYM+exR4BXtdblwKvu+8HIDvyl1roS2AF82v1vHQrxTwM3aK03ABuBPUqpHcDXgMfcsQ8BDxgY42L+AqifdT9U4gb4oNZ646we9FB4vwB8C3hBa70a2IDr3z9UYv9vWuuQ/wJ2Ai/Ouv8o8KjRcS0RcwlQN+v+GSDXfTsXOGN0jF7+PX4D7A61+IE44Aiu/Y/7gYj53kvB8oVrd7ZXgRuA53Bt0xn0cbtjOwtkzHks6N8vQBLQirtpJZRin/tlihE9829gfskm5EEuW2vdBeD+M8vgeJaklCoBrgKqCZH43eWPY0Av8DLQDAxrre3uQ4L1vfPPwOcAp/t+OqERN7j2iX5JKXVYKfWg+7FQeL+sBPqAf3eXzH6olIonNGJ/H7Mkeq82IRe+o5RKAH4BfEZrPWp0PN7SWju01htxjZC3AZXzHRbYqBanlLod6NVaH5798DyHBlXcs1yjtd6Eq7T6aaXULqMD8lIEsAn4V631VcAEoVCmmYdZEr0ZNiHvUUrlArj/7DU4ngUppSJxJfmfa61/6X44ZOIH0FoPA2/gmmdIcW9qD8H53rkGuFMpdRZ4Clf55p8J/rgB0Fqfd//ZC/wK1wdsKLxfOoAOrXW1+/6zuBJ/KMT+PmZJ9N5sYB7sZm+w/glcte+go5RSuPYIrtda/9Osp4I+fqVUplIqxX07FrgJ1+Ta67g2tYcgjF1r/ajWukBrXYLrvf2a1vpjBHncAEqpeKVUouc2cDNQRwi8X7TW3UC7UmqV+6Ebce1/HfSxX8LoSQIfTpzcCjTgqrn+X6PjWSLWJ4EuYAbXqOEBXDXXV4FG959pRse5QOzX4ioR1ALH3F+3hkL8wHrgqDv2OuCL7sdXAgeBJuC/gGijY13k7/AB4LlQidsd43H310nPz2YovF/ccW4EatzvmV8DqaES++wvWQJBCCFMziylGyGEEAuQRC+EECYniV4IIUxOEr0QQpicJHohhDA5SfRCCGFykuiFEMLk/h+ouuZAhEP79gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kde = KernelDensity(kernel='gaussian', bandwidth=3)\n",
    "kde.fit(x.reshape(-1, 1))\n",
    "\n",
    "# Plot\n",
    "xx = np.linspace(0, 65, 100)\n",
    "yy = np.exp(kde.score_samples(xx.reshape(-1,1)))\n",
    "plt.plot(xx, yy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KDE in Higher Dimensions\n",
    "\n",
    "All the examples we have seen so far are one-dimensional (each observation is made up of a single feature) but the ideas extend directly to high dimensions (each observation is made up of multiple features). In 2D, for example, we place a 2D Gaussian at each observation, and the density at any given point is the sum of the values of all those Gaussians at that point. \n",
    "\n",
    "We illustrate 2D KDE with a toy example below. In the next chapter, we will see a Capital One use case, where we perform 2D KDE on a set of (latitude, longitude) values of credit card transaction locations, and use that to determine the relative probability of a transaction happening at a given location."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us start by generating some 2D date and plotting it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'x2')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate 300 data points that are Gaussian distributed with mean and covariance as given below.\n",
    "n = 300\n",
    "mean = [0, 0]\n",
    "covar = np.array([[10, 4],[4, 2]])\n",
    "X = np.random.multivariate_normal(mean, covar, n)\n",
    "\n",
    "# Let us create another 300 points by adding a vertical offet to the previous points\n",
    "Y = X + [0, 5]\n",
    "\n",
    "# Stack the two datasets together to create a new dataset of 600 points\n",
    "X = np.vstack((X, Y))\n",
    "\n",
    "# Plot the data\n",
    "plt.figure(figsize=(7,6))\n",
    "plt.scatter(X[:,0], X[:,1], alpha=0.3, s=10, c='red')\n",
    "\n",
    "xmin, xmax = -10, 10\n",
    "ymin, ymax = -7.5, 12.5\n",
    "plt.xlim(xmin, xmax)\n",
    "plt.ylim(ymin, ymax)\n",
    "plt.xlabel(\"x1\", fontsize=16)\n",
    "plt.ylabel(\"x2\", fontsize=16)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can fit a 2D KDE to the above dataset as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KernelDensity(algorithm='auto', atol=0, bandwidth=1, breadth_first=True,\n",
       "              kernel='gaussian', leaf_size=40, metric='euclidean',\n",
       "              metric_params=None, rtol=0)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kde = KernelDensity(kernel='gaussian', bandwidth=1)\n",
    "kde.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the 2D KDE as shown below where we first generate a set of (x,y) coordinates sampled along an evenly spaced grid, evaluate the density at those locations (using the \"score_samples\" methods) and then plot those values using \"pcolormesh\". In the output, the darker the blue, the higher the density.\n",
    "\n",
    "**Note:** If you are not familiar with the \"meshgrid\" function below, change \"stepsize\" to 5 and print \"xx\", \"yy\" and \"xy\" to figurte out what is going on. The idea is to sample the density along a fine mesh of evenly spaced points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'KDE in 2D')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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F0k5ysFzDk82gLItuKrWFrb0+Ji132czlMNeDBFIhhLiGusk0ht3Hm81g2H26yfHeZjc9Q+7Jz+LJ5+mmUnTTs7i3qK3i6myrQKqUOgz8xchDtwD/VGv9+yPXPAF8BTg9fOivtNa/d90aKX4mbeaen5uZul3r+tHzzvRlb0Kq1pmK7Vvj553pVmc6tt13nHdc31l1/tLznalaZ1udrzVxlu6E97oRznSnYaw/y3YsnRpO0Pr4p/EW8nSSKdrRBO7e+Afbi6UgNuyJ9izCxTyeQo5uMk03PXl9qOEevJ4rm8FVyNNPpwfFGdZou/N49b6sm5senXb/0vVMSuVey9ceta0Cqdb6Q+AeAKWUCVwAvrzGpS9prZ++nm0TQoir1U7N0L7CggneXJbZ731zZfJR5hc+B/OX0pzuXAZ/qbBy3E+lYecOXNkMkW9+DcPlQvX7VD/3zEowFdfWtgqkDj8PnNRan93qhgghxPXiKeTQhonl9RI4c5rgiQ9pDQOpO5ch9e2v42k1Cb77U5p33Y0VCNJ++guY+cHz+rNzuDJLuHI5CaTXyXYOpL8C/Pllzj2slPopsAj8D1rr99a6SCn1ReCLALt3774mjRRC3Nz8hSzBYp52MkUree3L8HWTaVzVMvGj7wMaKxigf+QIvfQs7nweDBPb60WbLmyPF22YmPkcViqNsq1BycB+n356+y8buVlsy0CqlPIAzwC/s8bpHwN7tdZ1pdRngf8CHFzrPlrrLwFfArjv/vuv3Vx3ccO7lptnX8sxUFhj3HPk2DEkuepa5/IV5ximc8yzY0047xhUXXU/6/Jjpl3Hua7juc7xXud5p40ubzHXGFALFnPsevk5lMskYFt8+OiTNBJpPI7lJ6PPDRRyRKtFWokUzeHEIp9jt22va7xekHekqe14ivztd6MbDZp792N0OhjZHL3kDK1EklDfwt1pg9WDbgdMk14yRT89Q/mpp/EVCljpNP30LOjJG547x3entZFxyc1ernK9xkSdtmUgBT4D/FhrvarMh9a6OvL7N5RS/0YpldJa569rC4UQN71guYA2DBrJGUKFLIFSgUZidU8vUMgRKObRSrHznTcx3C4Mq8+pJ55aCaYbUb/1MKEzJ/AWcriqVVr3fxSAbnqW3JOfJVwpUH78kyvX+/OD6j/9mVk6c/NX+W7F1dqugfRXuUxaVyk1B2S01lop9SCDMoeFta4VQohpNGJJlG0TKmRRtkUznlx1TbCQ49aXn0MbBuHMBTqhCLX5gwTyWfzF/FUF0k56huK9DzH/7JfpReLE3nyNXnKwNKabnqW1YxAs3bkMiWf/GrfHjbJsKp95GiSQXnfbLpAqpQLALwD/zchjvwmgtf5D4JeAf6CU6gMt4Ff06vnbQozZTnt+bmbqFtZP3zrTpc5UbNOxDKPZW/+8M1XrPN92pHbr7f7Ycas7fn40Peu8t7Ptq6osTTgGiJbzhCtFatEE9ZGeZKScJ1IpUI0mqQ6XnaxK1yoFrgj5uz9Ool6iHktS80Sh3sU1kkM0FxZp9DX1ZBKrVMZfLmNevEjXtmh2LfzvvYM9MzsWUCctxTEV9G2b5twu2ulZIsU8RjZLb/gerGGq2JvNYRsm3fQc7szSYOuwDQbSjaZXnVdfy2pD06Zqr1emd9sFUq11E0g6HvvDkd//APiD690uIcSNJVrOc9/r38c2DAzb5q2HPkk1liJSznPfa99befzHD35yJZiupRZP0VlnLWc9lsIY9lp7/iCnHngUr9sAFDvffRNtmHg/0Jz8+Kc31DvtJFNg2/hyGVCazhrP7aUGVZHcmSWwbfqp9Pb7Uv8ZIJ+5EGJbCZfyhCsFiqE41fiVlcuLlPMESwVq0QSVYVAMV4rYhkElniZayg16oLEUkUphzcevVj2e4ujPfYpguUAjlqSeSOP3mKRPfoA2TBrJGTzl/IbTvJ3UDIs//xm8hTzG7OyahRl66Vnyn36acLlIP5WmPzMrX+pbQD5zcUOaNpm/lXt+Tiocv3pmLeued6ZAR9OtzlRtreNIta5K7Y4fVx3XO1O1zuNV93ekclvd8fNjs3b7NvFKgYNvvYBtGOy0LM7e/XFK0UGCyvk56eFxvFrgrrdfxDZM0rbNy/c8TimSpKH9pGtt7MYFqrbNh3aAUrFJww6QrLdR7Ys0bItTRohytb1q1q53JNXr94x/VTrTwB1fDOZig4Nmb9BWf4x0p4crc5GeAaVwfOXzcL5Wz7EJqDUsUt9MztBMzhD2jM/yHf3vt5Oawb1jB1dq0t6ozr01N5pedaZyN3Mm7RZNyp1IAqkQYtuI1ga9yGI0RaycI1orrgTSy4nVithq8JxEJU+sWqQUSVKKJHn5nseJVYuUIwmqw/uUokleufvjpJplKpEE5Qn3v1r1RJr3Hxn0VJmbXXO2r7g5SCAVQmwblXACw7ZJVPJg21TCiTWvi1cLRCsFyuEE5XACQw+eY9o25cil5ywHVIDRPl0pmsTtMohWiwDXNJjWE2lCPvmqvZnJ367Ylq71Hp+rn+98/fVn3o4ebmXqdnB8+fRt3ZFarTtSq5VWb/y4OX5cdpyvtx3nHdc7U7l9R1v7XcdM3JH3pm1NET+lPQ+SqJcoBGIUe37IN8eek6gVeeCDl7EMA9O2ef62R/nW3ofYnz+HQtOodKjbbZSzsPxIUYRErci9H7yErUwMbfHSnY9Tde7KMkynxisF4u0y1UhyJeAGHKlWZ6rWWSxiUnGJjXKmZ0frPTgzt5OON5p6dV6/0VTutUzPTkpbXysSSIUQ20oxnKAYTqyMgTol6mUsw6AQTpKsFUjUyxRDMfbmz2MbBnvyC7xw+6NjKeFErUiqWaEUjlMMJ4jXStjKpBBJkqwWiNdKK4E0Xi0QqxVpDVOxD7/1Ai63C8O2+dH9T1yz3qu4cUkgFULcUIqhGKZtk6wVMG2bYihGol7GHgmu+7JnSTbLFENxAD7+3stgmhja5sU7H6MUjmNoi2S1gKEtSuHBdfFqgUfffhFbGXjOwcLMHmzDoBRLES/niVQLVxRIZ09/SPrCaXI795PZf/iafh5i60kgFUJckUgpTzyXoRq5tMRkKxTDCZ6/7dGVnmhxOI5qDINruFnn9uZR6sEIhm1zNr1rEAwjSXbnznPXqbd555aP8NKdjxOvlQa91EgCF+MTl2YaRVAaw7aJl/MYtk01MjmI7jhzjE9+5d9hmy4M6zm+98tfpHHbHWteGyjk8BfzmHOztK5wmzWx/UggFdfNNEtWtnIMFNYfB500RjqpUHzX8QTnGKhznNO5xGS9cdBiozt2rlAfP3aOkRbqnfHXGo6BxqsFDr/9Il0LErbNS3c9RjGcoNdxbFDtaFvfMX5rOcYKl9O3qUaJWKNEMRAjH4yPXZNqlEg0y5SD8ZVzdQKcDwYHf1HVDg2CfGvvgySaFWL+KnvKixS9UVK1Iv1OH7vTY8fiaW69eAKr1+eRSpGXPvI4H6T2DV6kY2Hbmpw3it3tEylksU04kdrLidReZtoVKuEEJX8MutZYZSMY/DcQKQ/Wvx766Q/xNBvkdu4jWC6SOH96zUAaKOQ48MK30IaJ/wM4+4lPrwTTVRuJrzMm6jzvHKNcdexox+ox1PEHnKOO13NMdKvGPDdKAqkQYqLlnlohEl8ZUyxeZkbtRqUaJX7+xA/pozC1zXdufXglYKYaJT514odYysCF5rsj55wKoQSFUIJkvci+4nlStSKGtjmd3svp9F7uOf8+AMVQnF35RfZlz6x6D8Vwgpfueox4rUQ9mVqZ8duc0FuMlPPc+9r38LSbHH73NaLlAqFKkUpyhvyu/QSLuZWCDcvLYPzF/KBgQ2oGbyWPr5iXXukNSgKpEGKi5SUmyWoBw7ZXxhSdkvUiiUaZYjBGITQ50KYaJe5deI9At83JxE7S9SKJZnklWCaaZSxlkAslmK2XOFA4R6JZphiIUXAEwVszp9hbvMDZxE6+d+gRZrrVsXa8ve9Odr+1yMeOv4FS0D3v58zMvjWDaTGcwOMd/3qMVwpEa0VAEfQYVKJJKsPx0vCwWlLf7aEZjpHdfwR/vcr5g3cQrJQ49NMf0A5HULbN0Ud/AQI7aCVSKNsimM9iGNBObF26XExHAqnYNJu9ZGXs3queO6ktm1s4fr307bSp20mp3LojXVpxHK+Xvl19zpG6dZzvtMbv3R2mfsv4qO58gFChQCEYo9D0QrMxlspNNUp87Pgr9DE5hMW39j9EwRMeu5+2L723dLPMo2d+hL/X4WDxDJ1Wh6bby4W+m2aljjJMFm0fD1dLHCksYQC+aomqL4xhW3z30CPkA4OAeyh/ht9466/oKwOXtvnSR3+JpUiSZKlIt2NTCMXJ+WO8O3cQT7vFQmInfnrEykXy/kFFIu3Il9ojlZMOFc5z6OwH2Ibi1nPHWDhwO12vn9cfeIJKLEUtmsSwbVy9LoZl0YolwG2y4/wJ5i+cIlErcfqjj+HqdghXilh7d9GfmeXcJz+DvzgoAdhPzeAevrbb0Ra3I9frNtYosL/G72sdr0rNMm5SaniSSZdfz3Tt9XopCaRCiCtSCCVYNCOXPZ9sVehjkgvGSTdKJJsV7L5FslWh4I+SCwwCVrpZJtmqEG/XsJTJqdigvN35UJI3525buW6Z1oCCZLOMz/KTDSbwAclmZSWQ7itdoK8MLkRn2VnJcNfFD/FlWAms3zn4CDVvitPpvewtXMDb72IaGq3g1ounKIZi1Lyr06rxaoHH3n6RmWaJ+dwFcvFZ/O067n6XdiBEpFqkEktRjaX4yYOfJFwp8P7djzDbqXL7q88TrFewDQNXt038whnqyRma8STe4f1byTStZJqQR76Kb2TytyeEmFqqUSLWrBDr1gBwYaEVPHnmtZVdVr6970G0bfHps69jKYNopwF6MPmo5fauGUSTrQpVX4isGedwaYG5Rol0q8LR+B4KgejgtZslAALdNjsrGVzapuoL4eo1yYcS7Cuc596Fd3nP+xEKoQTPH3mERKOM4TK5+9y7K4UdfnDPE6vSvLFaCW+3Tc/0EGzWiFULBNtN9p0+yqkDd1AdqaJUHQZUgPDSSSrpOVxWD2+rQSW9gzN3f4xWLE6gVMAT8NC6in1KxfYkgVRcsetZbWjaWbaTnr+R1C2sn751nmtP2NOzNqnakKMQfKk5nn4tOmbeFhzp2Wy1fem1HOcCSxkS9RLF0KAwQbt5ZandZb32eJUhq9Mi3arw+MJPsJRBt1XlqDvK8ehOUsUM7WaVjC/CbLtK4OIxANqtOhlfhJ5lcTqYpOAJUvCFyfd6UMmt3Nv0+FnSCtoNdrcqtJXBKzvuJNGu8VZ8N0vuCKlKnp8//SNsw+R4YjcLoRTvzB2hGIjy1LnX2Jc/z22ZE6AV6Q9+wPcOP0IulCAXiHNH+Ry2aVJcLuzQKFGKXgqMpsvAdBkcWTiG6Xbj63e5OLuHhV23kGpWOXfwLlqpWTyA3z1e6chKz0AwSHXHbnyNOmc//Xla8SS3vvhttGEQPPnO2Cxdr6MIvtuRT/U5z5uXn8XrnNE7qZLRtLN0r2cqd7tO4pVAKsTPiES1wEPvv7zSQ3zh9kdZNENj1ywvNXEuQ0k1B6najOkh5x/vNabaVSxlkPVHsfpdSt4QOd8gBWxqm9l2FVPbFHzhVY8di8yRHV67/P2fbldJtWuUwmly/ijf3HUvByuLuPInSbRrNF0ejsd3DV67VcE2TLKBOKbL4N25wxwbLmn5zsFHuPf8u4DidHIXc50yiUZ5ZfJRMRRfWXt62QlUWnNszyFcAT/h+g4CzQaRWpluMMjirltWXb68BRxzs2Nbq5m7dpA6/gHaMGikZvBXCzJL9yYigVSInxGxWmms+k+iXmIxeimQJutFHh8uNVlehrJohEg1S3z69I/oY6J6LZ7d+8BYMM37IpjaZqZVQenBuONt5QvkfWF+lNzPgWqWk5GZlYD5jR13kWzXVgLrbeULFHxhlGFysHKR+8rnKbn9eCoLfHPXveT8gxTufZUL+PudsR5Q3h/FsC1mmiVMEwrDawEKwTg/2X0nyeOvkK4XMU1NMRhbmVlcT6Z54fZHV3rotTWW85QjCTqeALjcGJaNt9PCVop2IDh2XbiUZ1y62jsAACAASURBVO78CfYcf49mKELwpOLoz32KzC1HAIgCzUQKZduDWbqmmjhL15PL4i3kBht6715/mzQzm8HM5bDSaZifW/dasfkkkArxM6IcHu+BLZfPW5ZoVFaWmiwvQ1kMhUg2L00i2psv8cDSh7wxd5icP0a6VSHVrvJa6lYUmn6/w0P50/SVItZtgbYpewI8VDhNwRsi64us/JlpV/lbZ1/H3+9gKGi4/PitDvvreb4/dxumUqTaVXL+KKl2lYo3xPH4LmaaZZKtKsXoPPlAnG/tf4iDpfO4XOaq91wIxvnOwUdINspU44NA+ckPX8EyTDyZD3nh9kc5MX8AYGXG7KjlrdhuLy6wY/EU3m4X23TRMgzClcFEo2g5z0feepFwMUcqc56j9/4cNn2C5QL1ka3Tmsk0Jx5/kkAxj3vH3Lq9UU8uy+x3vg6GC+w+raefoZeeXfNaVzZD6Ft/DS4X9Pt0P/8FrNm1rxXXhgRSsWI77biy0TFQy9EWZ9Mm7cDiHBN1LmFZbxx0o2OgzuUsJcc45EbGQAHKtfElLe3Gpfstj4Em60XMRoUfhA8AepC6bXtpN2or155pubi1UiZcrdLTNmfDXWqNs5xr17izmmNncYHbimfpRnbyifw5fhTfw4OFU1hKYWrNX8/cRrJdpd1ukPGGmGmU0Fqz4Aow22kSyZ9nITq/8nr7i6c5XDpHxe1nT7PIyfAc78Z2sK+WYW/lIoVwiqzbj93vknX7Maw+6fqgyELeM56SvqW8iOF1c6C6yHMHBkUbzOG4Yjk62LXF43dx68VT4HZRCieZa5VJt6tUh8HOuW50eeuznm8WS7VozswTxCbcaqK6TZidJep3syNTxetz09y3H09+gV35Bay5eYz5OaKBQXiOLN97xzzdHfN4vC4CI68VcIyxRipFPG433Zk5PNklVLFIe+5Sr3R0+Yu3UMBwubFm5zAzS7jzOZi71CtdvRxm7HDq5S5O04yJbtcx0EkkkApxk0vWiyu9MN3urgQap1wgxjd33UuqXUUz6A32lUnWF+EbO+7iwdwp7EifE6E0s+0aBxp5LKXIeMPMdmqkOg1ynuBgDLRTp2m60VpzsFEg2m/zemQ8PTn6j52O6UZpG5/V4/3wPD+O7qISSZNqV0m2ayg0r88cBK0HS2n80ZUvr+Vx0kIwQboxXtDBqRSKYdg2qVoBw1SXLSzhVIsm6HgD5GZ2EmjUeP/Rp6jFU8NzwzWk3Q6Z/Ue4cPgOOkdupznFrNxeKgW2hSe7BLZFP3X5e1npNFh9zMwSWP3BRCdxXUkgFeIml2hUsAyTfChBrJNdFWiW13UW/FEW/VGS7RrPnHudiidAXQ/GNLO+CK+lbyHRKjPbrmFiczKY4sF2ldlODVNr8t4gWbefv545QqrbIO8JkmzX+JvZ9ym7/DxcXaDgC5P1DnqTx0JpzvljxLtNjgVTfHXXfYAm7x2MnT5TOI6/3+Xu0jl+GttNxx/l2T33r4yZLlseJ003ikTaDWKtKqlGiZr/UkBJ1ovMluug4ExyMFFpcc+tV1zmsBJL8eOPfoJwpUgtmoD5Sz3rWjw1NrGonkiv9ESvVi89S/7Jz+HO5+mlUnhnLp+q7c/M0vjcM5i5LFZ6BlPSutedBNKfIdspdbvm+ZHfnalYx97XOPa6XpXanbScZSOpW1i/GtGkVK5zc+wNp24d1zcdx636OqndRpszLReHKk2CtTa9doNzkR61bAaAWHGBJy6+szLB6JXgLJ9Zeo+5domQ6eWkO0zYfZZzoRnOAX8VnCPVa5J3B8jgZiEwf+m424NujwVgwfBD3ybW73DWHWDJE2KuW+dg9SJJd4CcJ4AN1A0Plhtahof8MMCmOjUSnSaW4aJnQs9w0XV7sF1u0r0mhcigd+YapkPL0RTfPfQItzWWuGvpGLc0shyqL/FS9LGV2rtPnHqVMH0OX/iQYzsO0fL6yfsO4/Vf+gqMhTxjn2MscOk46ndDcAfNnTswgZgjUJqpHbR3Dc5FGUnlDoWcx44CDAG34Tg2YccO2LEDN+Bxjec8ncPBam4We24WxerU7erlMNd2uctG3KipXCcJpELcIJY3nL5ohDdUMD4XiPHtfQ+SbFVY0mqsR5fq1LCUsbLW80A9T8XlJW56CVkdYoaLnOfSaF7GEyTjGcxYne02SA6DKMAdjdwgoHouzWjNuwOYWjPXrRPvtUlUL1Jy+XFhcyyQwFKKgieI1+5zqJrhYHOQLo51WxhuH7ZSuG0br9Wno+2VWbnpZpm5RoZCIEo+ECcfiFPRTSq+0LAIwwIfOfsub++9k3ijjK0MeoZ7sNbV5cZWBrFakVIkufK56rk52bRbXBUJpELcAEY3nD7U6vHCHY9uOJjmAjF6jcrY43lveGxd58nQLOl+kzP+OPPtGm+HBmnCmW6ddLdJxnCT8QSZ7Tb4fOEEloZYvw0aym4fprb5auLAyjWHO2Vybj8ll4+42eauVpGLnjA+u0+81+Kh8nlM28IyTM6H04Mx1+EymXPxPZS8IZ6fux0FVBI7yQVipJtlPn32dZTXi2HbPHfgY+QDcQqBGC5ts6+wwD0X3udiu8ju0iKvHHwQQ9u4rT6mtvH0e1imi3I4Mfa5hi4c5Uf3P7FpwdRfyOIr5GknU4PepbhpSSC9yW0knbvRVO5m7/Fpj51zXDshddufcP00qdu1jkcLy5fbE1K3juNiYzwVm62OH7cc17cbXdKZRer1Pvlwgh3FMxx4+3WqO+8gH4zTdqSGu7Xipd+bg8A5066R6tRY0sbKGCVArdvhJU+Mg80ixwMJ3sbDYmCeI80C99Mk0ijxt6oZQlYXC0XTMPkPyUPEey16vS5L7gBz3RYAi54Qc1aLZLuCbfX4tfyH3NUpg4azw+C4v9fgQKfCe6EZysqPrQw6bg9uu4/h9uK2+8z1WrgMF6fnbh0usRksd3H7fXj8fuYaGZTXSzkxQ6peZIduUg/O0ggGeTnwOI8cfRXDZRAwYbZwjpMH7uTVBz7BXL/GO/c8DGgq4QTm/Bx7zh3DH/BSjqUItMrst+pciOwEIOa/lL51jnkuz+hdFvas3ilm58vfWSl+UX7qabojk4Ccs3Sdxz5Hqtezqmi9s7KRWvN32Pyi9E4bnaV7s6RzR0kgFeIGUAzGMLTN3vx5DuVOEuy1uC17imcPP8bbgZ3rPnemXeOzw3FQ1W3xamwPaMh7g1i9Ng9XFuhj8HBlgUxkDxlPkFSvSdntY8n0cLBS5ki7xBlflAPtNkcCJY7645ho5npNWqYLDcz1mriUIucOkO418Vs9yi4fAavHra0iF7wRvps4wP5mkTfDg8k6HdNDxe0j2mtTdgc4FZ7hlmqWU5GZlSD61Nk3sJSJp3yWN+dvI96uEmnXcdVduLRNYaQ+byGcYDExT8flBTQa0GqwNVo7OF6oIAZUoklM2yJWzmO6FLVN6o16C3lsw6CdnsWXy+At5MYCqbi5SCAV4gawXGz97nPv4qnXSbQqBLotnvrwZRYPP7myC8paRsdBb2lV+K+W3mPBH8HUmqOeMH0MMt4Qs506qV6TjCc4HNu0mes2cAEdwzVIbwx7Exl3gK/E9nGkVSLeH/SoSy4vHwZTZIZjpiaaQ80CiV6bi54gh5pFlOEi5wnyYXAwYej9yCz+fo+y20e821ypavRQ/jS15G6SrSqWMskGYhxq5fns8Ze5OJxsdD6+g5PJPRQchSXOzOzlxNx+QrpHNjbD2dl9l/1sKtEkr93/CaKVAsb8PNX45uwJ2kmmMGwbXy6DYduD6kTipiWB9AZ3o6ZuB+cdxyP33+zUbbu/firXOdO26Xh+pTOevq00Lx07U7e52visW+f5Wm1SKrfnOD+4voyXSvAWdtXfwt0oUXb7yPchcOEojdilXmm/Vb/0e7vBhW6X+5pVEs06oUaZosvLgm0w123Q6wOdOqlOA9AseeP023X6vSbvG14w4VVfgqeqCwR0n/MuPx94I2jbItWp8/nKeXZ3a7QMF+8GkhyPzGO4PBh2j4bLz5I3isLg9fhe7qktEVSaotuDyxcg6w3znxNzHKwscm/pHHe1S+xr5Hh+10dw9/vM06eQnMdTPssOq0ncblOPRKmmZvHU3bQTSVpzsyuFDfzhwSzbdmSe74efZke/TiWSwI4miQHJkJdRieBwVm48gMVuwgE3o4X/RtO5QUfq1TkLd1WqNrKTxuc+jyefp5VK4Zmbx7PO9c6i9M5Zuc5Ursu4fKp39azd9QsyXM9ZurD+d9aNmvaVQCrEDSQfiPO1vQ/y+bOvU/UEaLo8KzVr13MsMJiY9Ko/wSO1i8x1G5ja5qg/zlF/nHSvRc7tJ2N6me01+buF4wR0n6Zy8afJg/xp8iDpfoucy0/GHWC21+SXyqc50C4TtHuUfVH8Vo/DzQKpXpNkr0XZ7eP5UJJPFU+ys12lbbp4PbEPX79PqlMn6w2T80VItauU3QHygSj7aln2VbLkAtGVGbnPHfgYyWaFDwJu7r3wPql6EcO2KIZil32/xUiSXnD+suevh256lu6wrJ93wrXixiaBVIgbzNH4buKdOncUz3AiMr9SDH4tM906n88dI2D1iPbb/GVsP6+E57m1VeKEP74SFEcdaZW4s1WiaxjM9Fqc9IT5cuKWlZQtQLrfomJ6KLj9pFptZrpNLroDPNDIUnb52NWpEuz3WFLwXmiGk74Yt7TK+Pp9TOyVNaMwKHrvwsZl9fggvpufpvZzPL6LqiNdXQrG+N6hR0g0KxQDURobmLUsxLUkgVSIayxeKRCtFamEE5Q2YTLLkdJ5/vaJF+grg3uKZ8ke+DgFb2hlR5XFkXma6W6TgNVjf7tMsN/l1zPvU3e5sVEc6FSxg3M80shgoTDR/JfIblDg1312djv4LItHGhleCc+NBdKcy0/DcHPOE8LQNi+G5znji3Kw16RtmOzr1Mi6/MT6bf5q5jbeD88y06kzpwZBNOu91IvO+SJ8Y+c9zClNwR9Z2VnGy2D7tl84+Sq2YeArHed7hx7h+Mx+AHxTf5JCbA4JpNvcZlYjmrYSkbM60EYLx68qFL9O9aFJlYe6/fHjjS5faU0oNO/cTHt0TBQgOzLOWXBUFhotIp+oFnjojeexDYO9wz1Aq2q84Lpz+UqrVhs7dq793HXxKN1uj3OBOHuaJe5ceBuP1vQxiPdbvO5LcDSQJOMJsti3CLUq+Dt1qqYHV7/FR5p5znjD7Ot3ydqavlIsuf3M9Zqk+y2O+uKccwdx2xYZXwCtTG7rVMl6wxiuwUhf3uPnR2h+qXKG93w78JseysEk3pbN7k4Vw+Xi/dQ+AqaJJxjBE47jcbvwKo3XF8E3LKzgGfYqa8zRG45ZLo9T+gJudndauEM+8qEE4V6FXUaLTsy3cn5UKuIYA3WMiSaD45WLnEtaIr7x47Dn0kClc+PuSWOczvPOjbvXG+McnB87XGOc8/LjnpMqFzltdPnLZm7U7bTR7zunrRpjdS4x2haUUmeUUu8opd5SSr2xxnmllPrXSqkTSqm3lVL3bUU7hVhLolrglgsnSFQLY3uA2oZBol6a+v4ngylMLPY0S5hYVFw++hi0DRd31PM8Vr3AM8WTzHYbZNwB/nPiVoouPy1l4ELTMQZf8kpB2eUdVB7qNTG1XhkD/ZPkIU56I3hsm1mrxUebuVUpYBQs+CKcCCSxlEIx2AHm5dgtvB+aw2f3MLVN3hteWYJzX+E0n1n4CelWZY13tloxGMO0LVL1IqYe33w7Xi2w/8Jx4tXC1J+pENPYzj3ST2it85c59xng4PDPQ8D/PfwpxJaKVQrc/fZLWKaJaVm8s//OdfcAvRrvR+b5/QMf50Ajz8lgiou25vO5Y9zSKqKU5pQvhk9bpHpNbMNNst+ibrqwUDQwyLr82Epx3h3kh6HB2srRiUQA7waS/HV/Dx9vZDnli+CzrcGEpJENvXOuAKYucGuzQLTf4bXwDrLeEFlviGPhNKlOg3J0hqwvzO2VRSxlUPRHmRnuYeosPr+WQijB9w4/QqJRpjU7u1LNKVEr8ujxV7CVgaFtXv7I4xCR6kFia2znQLqeLwD/Xg9yj68qpWJKqXmt9cWtbthGXc9C8pu9nMWZ6p14fsKSlb41em5S5aGNVSZy7gFadRw7U7eTqhGNnm/ULv0eXbxIo2WRD0dJtYo0qx2+seMBEs3yYA/Qnp9mfbxnN1qJCFZXI7po6bFqRL12gx/j5sfDWalWr8VfBec5YhSp2zbubgO0xuo0+Xwjy4F2hcPdCt+K7KLr8nHCG6bg8pFz+VfGKpd/mq5L6c/jkR3cTo+AUpjapBRO4R3pEZaJ8+NwhF899zra5eZzzQwt72FyvghV0lQBdzCKH6j7fPjbRXYZFoY/QGN+P4FAHN9IujXgKBrvCw5Srb3ETjLsJBL2sjy9aG+jSTTspxJPEy3lOGK26SaDY893pm4TjtTupMLxo+edqVtnqtZ5fnS/UFi9nGXSHqHrVS6C1SnM0XTupP1Gnalfp0nZUed30LVM9W7UtKnhq7VdA6kGvq2U0sC/1Vp/yXF+J3B+5Hhh+NhYIFVKfRH4IsDu3buvXWuFGCqF40TaNWZqedpuL8VgjLwKX3Z/zMsZrUZEu8FfzxwZC6ZOGXeAjDvAUX+CZLsCGg52Ksz2miSsDsl+hyfLC/wgPMfR6J6Vnud6X4EZT4CvJW8lNUzppnpNXJ3BGtXlbdISvTrpXoOy28/ttYscrCySW2MWcc4f49m9DwzWhg6XtUyjEklgLNhESzkM26YWTcgSE7Fltmsg/Tmt9aJSagZ4Til1VGv94sj5tf7/X/VvkWEA/hLAffffv0X/VhE/azSD3v5G/oNLD9OdeV+EC4xXI0p1WqS6jXUD6bKMO4Dd7/KF8lmCdo+PNvPUDZOz7hBtDE54wytLXtL9FnlPaGw27qr7DXdy+XzhBEGrx87chzRdbhZ8scGYZTCB1oP/HQc/L/2vmW5XmetUVmbi5vwxqsHJ7+FKlKPJsf1BK7EUUoBPbJVtGUi11ovDn1ml1JeBB4HRQLoAjHYxdwGL16+FV2/aVO40M28npW43exausxrRqlSu47gz8oRpisivdb6ywT1BnTNxK8Pr48MJRC7Xpa3MRvcDnc8sUcBHJxBld3mR+TMnOJY8PHav5VTuIHjW6DYrPFQ6h4WBic1XYvtYBO5v10m2m9BtcbFv021UAbCGReKXzXRqY2Oc6X4LSymO+WKEbYv9nSpBu49lKg72W3ykW+OR+hJ9wN2r8bXkrSsB0+Xxj93b5Quys9oj6vawr1fnlm4FX6vPV2M76Boumqk9HKdPoN8l6/Jw4ZZ7CAbipJolnsy8jeH1YDYX+M7BRygE4yvp2mW+kT0/nedmnLNwg+PHsVAc2EOMQd3chCM1HJ6wB+jorFxYf6btpNStc89P56zc1enW9c9PSuU6U8PTFp6fxqThpmtpu6SVt10gVUoFAUNrXRv+/iTwe47Lvgr8I6XUf2IwyahyI46PihtLvFrgsbdfxDJMjrTX3sqsGIwSaTc4nH8XraDt8vK+f3Zl+69kq8LFYW3Ezyz8FMtQzJYuUHX5ORFKM9uuke42eC88y9dSh0l3G/Q6TVK95T8trH6XoyPFFJ4pn8VSClNrXgnOkOy3iQ3r32Y8Ad71x7mzVRpMGtI2t7ZLBKwubcPEb+mV+rqXk/eGiPRaJLsNQv0ObqvPJ5fe59X0rXw/vpMT8Z0kW1UK/giVYco22axgKYNCKEG6XiTZKFPYYHpbiBvFtgukwCzw5eGAuAv4M631s0qp3wTQWv8h8A3gs8AJoAn8vS1qq7jJRMp5IpUCliu8al/KWK2EZZgUI0ki3SyJemlVIC2EEpyNzrKzcpETyb30XG6Sw6UeT555DdswuKdZ50Q4jWUosv4o/nqRaK/FbLuGiU1uGNSWU7mfzZ8kYPV4uHYRG2iheCeQ4D8kD5HuDXqfS+4A9zVy/IPc+yy5A0StLie9YV4dbgmWtjrM9FrE7D5Fl4/7mgV6gNsw+W5837qfSdYb5ivzd/H3z/wQZbpomV6KngA/ie9ZmcW7/HO5T1gIRIl26uxaLNPyeCkEL1/OT4gb3bYLpFrrU8Ddazz+hyO/a+AfXs92Xa1JWY/rWUh+swsuTCqa0B/Prm5oJu5GZ+E2nKncCbNwnaneQr1DrFLg4E+exzJMYq0uL33kMYqRQTBtN3osGSEOt7qEOxmsdpdFFaBV79AambWbapTYkT2Pv9XgroX3+SC+m4uhvaTy5+h2W2T9UZL9Nv1OAzpNkt0Wda15LnErCsh5giwqE4bp23izSM+2aKFxWT1qpoey6SVg9Vfq47qU4nCnykdbBSwUR7o1ci4f93YqvOE7RMYT5Eem4hdzH1ILxLi/3+BUeJaCJ4DfNPEGY/gig11PPMHxJSnu4fHZmT38WWKeLyz8mKo3SMvt48It9xJJjfcyvf7BV0rE28YXcOMFtMdNJOGnHw6sKqIQG0nHOovKOwsoOFO3cb9jj9AJqVznrNxJRRVG07fO1O2qWbcTzm80Neu8/nou+Hd+52yP5OnatjKtPGrbBVIhPLkM5lKGbjJN5zru4RitFrEMk1I0RaCbIVYrrQRSGOxp+cLtj5Kol7hoBimEVtd6TbYqg/HJ2E5i7Ro/TR1YWS9p2pqZVgW05lh4jmPhueHyFsYnEo2MgebdAVyAz7boGSZebRGzOpz3BgdF5ofbmT1Su8gbgTSH22VS/Ta2MqmYnrG0bcXlo2eYw3KANh3DhTbdY3Vv13M0sYdqYo5ks7Iy8/ZyZfoSjTJVX5iF9AzJaoF4bXXvXYibhQRSsa14chnS3/4GHRTK6rP0qc9dt2BaiSQwbYt4JU/fsiiHV4/pFcOJwSbRjhKCy7SGuwqnsZSJqS1Kw51Zcv4o39x1N6l2jYsasr5BtZ9JMp4gX4nvJ91r8p3oHpL9Ftq2x8ZI070Wx30x0tZgXDRs91jwBIla4228p57FNl240Py/83dTcgcoRdJjdW8nyQfiV7R0ZXkj8mS1sKoikRA3GwmkYlvx5PNo06STSOPNZfAUctctkJajSX547xNEq0UWXaGx3uiVUgreTd5Cx3ThtcbTzzl/lJw/SrdZYaZd43NL72EpBZ0mX0sdvuzyluXlKelek6P+BEvmIAU62O7sGH6rT8t08WxkNwThpeguPlG9QMV083B1kfzw+T8Jpem7/Xhsi5I7wHvhWVzey08yWk+qWSLZrFBPptecRLS8Efmc1aAUjktvVNzUJJBusu00JgrjS1Imbaw9acx01XIX55ipY0zUuZl2x1q/OlGt06cbiePrdGFxka5tUQrHaXf6q4rKN7rrVyYqO46LjQ7Rcp5ItUg1kqDgiRKrFIhWi1QiCWquQa+s5gpzPhEmsJRhV/YoxdAgCHQcY6qd1qXX746M1140g9SVwtKanlJYvQ4P5X6KUnAsMkfWF8HudUk0ivRsm4w3TKrVJNWpkXH7menWSbQqK8Ev1WuiLYtHahexlEGstsgbwRkKbj+fKJ/lk7WLLPgiePtNfmwqXozt4e5OlUX6ZLwhdlg9dno85MMJet0q2uOjrzW1mX34fRHcgfExUW84shIkC4Eo9TXGQJP1Ik+c/gm2MvB1z/LCHY+tBMrRMVArHaQR8uAB5oaPOcdBYyPjnM4x0KhzDNTjHANdf/nKpGOPa/3C8aPjmBsdA3WOaU7cPHsLx0Sd3yHOtm2PUcirc73GdyWQim2lk5ph8VOfRS9l6CRTtFOb0xuNlvPc/8b30YaJsi3Ycye3n/gplmFi2haNw4+s9EAT1QIPvf8ytmFgDHdsuei6svRnPhDn2d33k2wP1nw+ffY17sidom26eCu+l7/Y+1EWMch7Q5jaZrZTQ2GT8wRW9g7taZt4r40Gym4fu5uDcdeOMri3kWVfq8KBdomA1Wem3ySoLZZGtzjzBHFhM9upY7rcK9uWfX3uduawyfvCa1YfgkFP88lTP8JSBqa2ecH/2KoeZ6JRxlYG+XCC+W5l08c/g8UcgVIec36eVjK9afcV4lqRQCp+JkSqRbRhUo6liJXz7Fg6uzKxKF7Jj00sitVK+Lstei437n5vMLkoNgikyXqRRKPMRSN02bJ/yynch5c+4M7iObxWj4DVZVc9z4O5U7wSnh0EttnbSHXqLGGQ9YS4o56lj8GSJ8COTh3QHPWkmG9Vub+ewVaKHd0GAbtPstdGK0XB5acHLHjDfBgYtD/rDa2sQR0dA816w5T8608sWl7/mQvGSTdKa67/XB7/TNWKmB61qeOfwWKOgy99G22YBD78KaefeEqCqdj2JJBugvWytdOmcp3VgqapRuS81+pU7/qp3Y3uEXolqdxRrZ6FL58l9b1v0taKiG1z+olP00rOXDaVGyrmCJYLFL1RavHUpfOOVGzFG2VPp4cvl6Fr2+T9IfZkjuKuVWl7/eS8UXqdQXt7PZtDC8ewlYmhLV7Zfx/9nk2yXuKJ46/QVwa3d3s8d8vHyAfjaHv8fa4c2xZd00UACPbaHGjkOdtKk2iV+frc7WT9MZRhMtsoY+o+xWACTyPDDqtL2+1HKdhhdfG4XLwV203XMHmsdBaXUrQ9fjy6T83l51wwyevpg3jDCXzeMP8/e28eI8mZpvf94sj7jozIzDq6+r7IJjkccnj0kEPODJfkDI/RAru2AEsQsAYWFgwIBiQYhv5ZWDKMNQwZWmBhGYJsQzJg2DJ2V8M5yeEc5HA4J+8mu5t9H9VdeUTed2bE5z8iKzszsqqys7u62WzmA8ywv/ziqqiKePN73ud9Xk8gTI00NcATjDFqAOgNja+sR52FAHrCS6h2lgAN5KBKKOHny92rwzynP+jBMkK8m3yGeK2IyGTwxpLXRd3CpJH86DjiVYmv1YgGfbSMNMFinoVmhcqOpcH89TsRbTTvpmNnMZJ3O+jMZdcU4QAAIABJREFUSuVOg/s1YU85/kSKZ4TEdFOzE9St6y3ivtZpVO/Nwn38m8G0a7tdtPQ8kM5xR8FnFhCyQjNhECxkCZgFWsmN6d1wMc+hX72OLcvo7R5nDz+IhKAWS1Lxj+f+yrEkv/myIyQCid3H36UeiBBq1fnDoUfGqElJwImFfXRVL97+NeVrslmmL8kUwhqJUp5kqzK2Kl13LloTEvlAjFOxRd5L7iZRK6B361wMJTkdSWPUTPSB+fvfv/wu/m6LluLlJ8Z+TgV1bKvHSX2/c8xug99HF3m8epk+Mp+EDfRem499IRQBx8MGut1F67Z5Ye0TfpC5Z+qqcyusi4S0RhkBfOXCsWs0771P0gymAShFk5SiybE60O1AW9ORbJtAPossQSepT99pjjk+Y8wD6Rx3FDpJHcm2CBaySLZNa4sXaahsYssy9WSK0JlTPPjWj2mFIsTMLMf23M/pww9SiV/bvxxLUo4l2XnpFLYkczmzE61SwP29tRRJ0PIGsCUZa9AE+0DuHAJQhc0u8xKhRo33046HrtEss690mQcKp6n4wtBu8KPlB8kHYvx/u48Sq6yBJPGoeY50u4qETcEX5kAtxz3VNcqql3Qjz65miawvRENSOBkyhr09AQreEAcbeRL9FmvBOLFem7/LHAEBj9TWyPojpNs19E6d9dbhRrtKpl3BHFDN1wszrGGGNfZnzzo2f9HksBa0mU5f93FuBG09xcWvP4+/WEBKp7ctRz7HHLcS80B6A/gsqdzp9KxrPHI97ktz08Bb7Qs3T+W63Yk61uR8M5ak9bVnEdkcLU2nGUtC36LedtHAXYtCKEGm18OXy+KpVejIMqnzp8hcOUvs4lm0tYu88cSLVGJJWiOq36w/xq6+RbxcQLIsisE49sjPVggl+PnBa6uyBy58TNdyguhZbZnHLrxPyRviqYvvsLO0ynJxlaDVZaWyxps7voRmVXikcJY/ZA6RjxjDYFgO6+jtGjmPn5I/itKpIisqsuoj1ioT61axfAH2dusco8tbMedLQLrbQJf6eKUEdcmi5wmQqOdZ8Ho5FVskSIsVSUHxxGguHSSUWERvlngudwzZ60VuX+W9wGEAaj7PmJFEMDJOxY6qbvu+RRLN88REHTnkwbN7ib2ZcWp4FuoWHPp2FIER+nVIxa4sw8oyflUeo6XdzkQ+ZWsV7qzuQ1sZy8/qje6mXt2wp+hJ3VSuSxA/SS2PNqdga4XwNKrXjWnXejOYdp/cmEZDu3G7zPzngXSOOw6tZIrGddRw1hM6xx7/I8LlArVd9/Dw268SqpfoeX1UYjreTotYxaQSmzzWBWMHSHAxs8sRGbXGA/XoqsyWZArhOLvMSxxaO03VF8b0RHji4rssVbIEOk3eS+1npbrG4cI5jFoBgYR+8R1+vPIQa4pDf66vCvWG0/3lVGyBT2JL7KjnsAXIkvNWkJCIdZocLq+CJPFY8QJ9SSLRaxHqtdnZclbHTcUJpD/e+fDQND4fiOPBEQ31UaiENXabl3nu5FusRQy8efjZwaMbujK5UYom+e1DTxOtmlSjzmp+9sraOea4+zEPpHPcMnjzWbyFAl1dp2vcGkqwntCpJ3TKA3GRr90kUVhD7XXo+gJjQTRRMdlx5RwHLx6n7AujWBYXM7vQqiahQmFYMzqKdYXqLvMSX1o9TiEYQ29WuBAyQMApbYX7r5wg2a5xIrFCyRdhzRPmbHyB1HrONOyoTo1WhT899xv8vSZt1cf/u/MR3tN28Hj+U7qqh8VWGcXucz6osadpovVbLDWLVL0hzkSd+1fwBBCKyvlICp/VQ2/XOKUtDU3j12EGY6hYGPUi4W6dui9MPqyR6VXQGuXrCqRwjQ6fY445Nsc8kF4HbsZkYbupXLeSdtr86LVN7DsjtTuNyh01YPDms2ivfh9kFew+2WdeoBcffyGP9h/1F3JEcg6d20oadF1mDu5xxzW2bMHFHfspf+fPWLx8hnrb4vLSbsoRDWxBomJy9IM30ComC4XL/Gb/I/josrJ2np25S3RthoKaYkRDHihAS3GdN+99gseO/crh/lQVoUgUojqVqIbt93M6tZsP0/s5ozktcr95+tcs2m0Un5easYTP66xE76lf5UizQMUTINY0OdZvEVMUqmGdS5EU/fJlLhp7OG7sZVctSzmYQCt70XttuopCzOvhQiSDv3SBA1aTttdPe3kfUW3SNKFPiN8kg6T7dU4jcf+FY+yQ6viCCv2VReJRx9Eo5hILTTOOvxnqFiaN4X3K5j0/3Spc97y7Z+c0KleeQlFOPqvXPpm2r5t6nQrXs+Wmat3P6jRVsBgZSq6fxP16mtjXfWzXeBr1ezsxjQqelfrdLswD6Ry3BJ5CAWSVTiqNL5fFZ+YhvvHKxl/IsfLzH9MREpJtce7p56mHb6w2sRrXqcZ1yi4v3FitiL/Toqt48HY7LBUuU4okQYClKJjh+Kbm6mZE43Jige5FL0gSPcXLycw+zugrJBtlsup4Telrex4dM3Zf73AuDf5v9Nk+H1tEEb9nRy1HX1b41dL9FEMaeypXSTVLNFU/b+38MlqrygP5Gsu1PPtLF7kUSdP2bGYZP7jusEYtMFDZhuNo9RINw6B0A9aHtxOefBZPoYCcTtFL3Vpx0xxzbAfmgXSOW4KeroPdx5fLgt2ns0VRvb9YQMgyfdVL7NJ5Emc/JX//o9t8RRL7Lp7EVhQkAWcW9vDxnvsB2Jm/NNVc/ZyxwuV4mnizyuV4mjP6CmYogRlK0HPVw25m7H4qsYMTiRX83SZXQxqnE8vkg3H+1/u/w67KFc7HFjmR3IkkK7y26xGSLUdxW4zqHCycp+yN4LV6NFQ/q7E0XcXpdVphumHButm+u43ZnQZPPov+2g9AVlCxKT334jyYznHHYx5I59gQSi6LmsthGQb9G3iRdY002WdewGfm6SQNukYKBqpdXyGHzyzQjyRo6ynamo63WiF58hMkCfqBIKtLe2hsq6ON4PSOg/Q8Xjy9LquGQ8PGayU+2n2Efteeaq7e9AaxJYW2x7fpNluhEEzwNwe/jlYrOCUpQSeveSK5kxPJnWPb5oPx4bzCtZyn1+qhChtvv4clK5gzlLV8HuAwGQrdVAalkEUt5OeBdI47HvNAugFuplfsrKbz250T3Srveb05UTWXJfSj72Ehg21Tfv5F+qn0RGPunuvk7nEnaVwLhragZwv8hRzLr/xH1FaTuNfP6Rf/lIaeInfP/ViNBtUdu1A6HXzFPJYQBEsFmgmdynW07hqFO7/mURWinTpNJUo7GETxKDz18a+wZBnFtvnF4a+iAgdz5yhFEuRc4p1Mr0EzGuNSJEmyZrJg1agHnJ8t3S2jNSoUQzHMsIblyiWLkd9ZK7rAamYBgM3ceyVX7k/1yHSTQd5OPI3WKPOR5ygIh67tRjRirobWXv+18bQcqNsYPuk2jnetYGc1hvcpW+c5PSM1Jx5ZRs2k8UoCj5lDRaBk0sN93DnRqTnPCbeg8Q9k4cqnbXEs97Oz3ZhWpjGRt5xoFD6y7Rb5UwDF9daZtVzGjVlLTG6ls5H7/Tqrw9SNYh5I55iAUsgjZIWekcaTXUMt5G9oVboRomdOEvv0OL1oDH+5Quzsp7T0FJU9B4h/9B7RS+ex/H5AGnqu+moVgrvvIb9zH3Vt9lVqrFzgntMf0AhGCDWrvHvvo9DtY8kyxZiOVimwM3ueQ5eO4+90aPt8/OBLz42tTovhOIptk6yZKLZNMeQE2mS9yFMn3x6a3//s4FFy/s2DfnLoXxvfsP3YxPb1EqluhWIoPizJUV1WeXcT+qk0pedeRC3kkdKpbfu7m2OOW4l5IJ1jApZuINkWnuwa2DZ9ffsoVjH89iuxuV5QIlBxTOb7Xh87zp5E1OsYq+f55OgzMwfTaLWIJSusZnaRqBRACMpRDcW20SoFFNsm0qiy98pZaoEIS2aN+6IfctnYMaR7ixGNXxx+Aq1eRkhOBxRw/mvJCoWwhl4vojUqmwbSZKPEM6feHjb9fn3/0S2DabLubC886jBIX2/ZyucZ/VSafio9tlqd4+6GlF1DzuWxUwYinZm+wx2GeSC9AbjLXcTY3Pi20/qHToxd55qVyp3oGboFtetmq9ap2V4yRe/ZFyGXpa8b9HQDbHuCunUfz31f3NcOUNt7gPL+w6jtJm09Q2XPAcARHHWjcZp7DhAs5JAlCVXYRK+cRwIqS7tQuh2i1SItPTVB3Vr25qs0n0dluZIj0WvR9QWwDINeMMF7j35j2I80c/EMiirj8cgEmj2+vPoJut1EXrN56/6vUYgkaEUytKoenvzwl/SQkPM2H+0+QtCnsNyvIfsUOgsZouEAAFqtSKJWwgzFKUY0VjpX8IT9VAf08IraoqstIrspy0EA2dW7ijfqp5ww0KomR3o5qt0OzbBOaaS2M+wff4zjI0b0buo2Pq18xUUTz0rVTlDq8uZULoyXrLiN4d2Ylap1PysTJSZ3UFnH9P6kbtN817M3Mu0u+5nWlXNWqtd9tJulaqXsGp5XXgFVQelb9F5++XMXTOeBdA7AyYsq2Rx93RiuCHrbuBJdR1tPceE7/xk+s0A5mqA18FJ1zMotgoUckm1R3LWfVkwjc/x9JEugdDvItk1jgxKacKlAPJ+jFkuOdYABiJYL7D/5Ps1ghFCjxkf3Per473atMbOB3qLN+aV9+LotLFmlEEkOad94rTgsb4nXSk65TChBsmoiCXjzyJMkaqVrYiUh0GpFnvr4l1iSjGTZvHHvExTDCeQBPSzbNsUpJT6liLO9VjWJNKscvlilFozivSR4+4GnxoLpHHN8XiHn8qAqiMwC0tpV5Fwe6yYDqZRdQ8rlIZ26LUF5HkjnQM1liW4gLrpVaOsp2nqK1oj3bktPce7p5wkUC7Q0HTp9lo+9g63I9EIhios7KOzcP0HrhksFjvz6J7SFhGzZfPDoN8eCabTiGNtnF3cRLxc2vaZSLMlPH/82sZrTHebAp++jVQrIwnZMHQYoRxIolkWy6gTDUiRBMaRNqH0TtdLQ8F2rmGj1EqcX9vLGvU+g1Usbuii5UYxo/PK+J0m2KiznLrHn6hnMmI4qesRqxXkgnQMlm0Up5MBIYd3ihgK3CnbKQOlbSGtXoW9hp27uC/z6ClcoCpJt0X/5O7c8mM4DKTfnXDQNE1TvxLm3VtJOUL3TlLdbuBNN0MSDbZVsDguZVsoRF5HL0tONiZ97csx1wSl3yVOLJ8e6ebidaNp6is5gPnr8GLKq0tJTqJKMretYmQyB9X0HfFOqVcbr9VCL6USKeTLtMvgzeNcpxnSG0NljeFolZFVCziyghXyE/Rs4J0WXaOL0vjyZMlhaPYsAjKgPJTo4c2KZ4/FnCZULVKNJ1FgSfeK+CoSyQKRwkqBVQwkqsLKIHguCHqQm78ADrL/23GrUMXo0HSbWLHPfpfdYruc4VM+xtvsg2T0reBKO7jfoEh+NUr1u6jY0TWU7paenR3FTt5Jr3k0Lbu0+NIqJ58zVlHM6FXvnULXTMOG6NKXf6aShvlOi5v/BK6CqyJZF44WXsVJpJu7DFKp3KwN8mJ3qnRUinaH38svbliOVcnmEMljhZq8643kgneNWoz/IgXqya843uG2kdH2FHIuv/xChKER7fVa/+a3rao3VGlC9oQHV20xs3E6tEU/ir1VZyl6l5w9Qd1G/tYTOR48/4wTyDajfrbB49SK2orB09SK/eejpoW9vJZbEnLKaLMeSfLLvARbXLnAls/Om/GqjFZNmOMrHXzqKcfUiF/YdmennmOPuhJLPg6pipTPI2SxKPjcIpJ8/iHTmpunc4bFSBpJlwdpVsC3ETa5wrwfzQDoH/VSa8vMj4qJtfBh9pvPtsG2kUbJr+MzCdQXSZtLgzFPPDanexhaBS0iTX7ojpQLhskk97gTPaYHPjWi1iK0olOM68XJh0y4ymyFeMbnn9AdYssI9pz+gEknccDCtxpLIto2n26GaMFjbsfeGjjPH3QXLMKDfR8mugWVhGZ+f3q23UqW7vsKd50hvMW62tnor04WpfQinqHQnqd6t6VQ31atksyj5/NCRaHTaTfuOGiz0dAN7vYn2YCf39tPgpqc8ioxtpFGFTbCQxxI2lmHgkSV8hRyxfJ5OUt8wsCoSkMnQzmSQgLC1sYm93ihDIkFpzwFCZo5Mu0Kz7WHfez9HyArSOYuTTzw74S87SXOPjwMry2irx4l3q8h+meDKMkuJ4Kbbu7HYWEWLBqlqBtFiniNqmyuG05fUTeWqrrHXRa8GvDHM5IsESybNRBItlUYbm3cZw4/whtOoW5/qom6nULVuanaa0nZaemAU0/7eZk2x3GoTha2wFYUNG1Derm+CU9XOskRPT9H/1ksoeafm1jJSzrNru8+9NdU7YUwxYeCwvbgele7NBlqRziDSmbkhwxyzQ8llCf3wFYSiIll9mo88jiUElj5u86fmHOs1tOQtt1/rGCnWnnkBr5mnFtfo6CmH7v3pj+hLMpJlUXjwKyCgGtOua7U6CiFJRNZWketVev4gzYROsFRAyAr1ZIqwmSNYMmc2ah/tdVqP69RmXE3WBqvIaDGPbNsz7+9GQzNoDIRW3inbzvHFwbDm9nZ1sN4GTFPpfh7LYeaB9C6Cks8jFJV+OoP//XdI/Lt/Q3vvfkQoRPVbL9FLplBzWeI//j7IMgGrf1tMwTtGyvlff+C1axZAlmnraSLnTrPj1VdoLiwT7/W5+PXnrzuYBs08Sx+9QycSxVetcP7hJ4fBRrItwuZ6fvXGgth6r1Ng5mK5WkLnw8e+SaRizpybneOLB0/e+XLb1w16t6h3752CaSrdW1EOc6sxD6R3ESzDQLL6eE9/SuC9d7GDQXwXz9NZ2YVSyEMy5axEZZleOoO0dvUzMQXvJHWwbfz5LGq1Qi8apW2kUdeu4i9eXw4VIDjoGlPaudfpMjOgsBqawcknnh1SoQ3NGLYyux2IlArDAHpl18Hbdt457lyst4br6fpEoPTks2ivfd8p17Asis+/COmFz+hKbz2mqXS3uxzmdmBqIJUk6dvAfwssAZ8A/5MQ4m3XNo8Cbwsh7goT0Jspd3FjWrnLhOJ/6v6u7UfGtpGm8u2XCPzmbeQHH0QxTaRaHblSppfUsYWgm9QRtoWSXUPMqNCdyIFOyOqnYD0fl1nAfPZF5HyW6oMPo7/7OyJmDlsCKZ0m4FEmqCp3Lq/nsfEsZgidlAhUTVAl/EsL6ING1FZwGbGyTAAIsIHr0nW4MG02HzTzjpm+ptN0dagJmnn2HfslQpaRLtmc/tqzdFwikGkNqSdzze77vnX+bPTeTS9XGZ+fNEOfLQfa6299H7dqbD/5O9r6XJP6gc8uJzqZ87w29uVzaD/9Ibas4rf7rD3zAv3Utb+JyNU1Oih0k2m8uSzW1Rwdbfxvxie2dpQadT6SFLfzmsvEfoq72u1wZtxKpbtVoJ1q7n+bcqJubBlIJUl6EvgecAp4B3gceFOSpH8hhPgXt+H65pgR/VSa1mNHUYsmdjgC5QqVl//YyZFaYswUvJvUP7MWVR0jRU/T8RVy1HbvdbqZ7DkwU460pae48PXniJ39dKrIa7sQNPPse/M1J1DaTqAcDabrq+SGniJUyBEsFiYC6RxfLHjNPPZIk3uvmR8LpJ2kU67hzWWRLIuuPk8DbGc5zO3AtBXpXwA/BP6eEMKSJMkD/PfAX0iStCiE+K+282IkSdoB/Acgg7M4+7dCiL9ybfM08F3g3OCjv50H9WtQc45qt/nIYyCgm9QnXIrWBQo3o2r05J3zbERVXS9Ga0wly6I08N2dFfEL57BkidiFc1z4+nO0krcucG0UKEcDaVPTkWx7UP9q09TmL8UvOrpJA3nQ5F62+3RdLEbXSJF/9tt4CwW6uk7XSBPcggreCmoui7foqPY/rzWln0dMC6T3A/9ICGEBCCF6wD+XJOkY8H9KkhQF/uE2Xk8f+KdCiHclSYoA70iS9BMhxCeu7X4phHhxG8+7bZjVwHnm7bdwb3FUu99zyj5si+q3XqKTTG3daHEEvnzumuAhlQZ543NtlNPpGekJest27e9xBW5fpYjH46GTcigtrVqktujkhnq225TeTeM589F6Gb9PpaGn8eWz6PUKlaWliWuelfazN/nF+HcsEjv1AdFaEckjUduxiDra4zO8TP2Fl/CZBTpJnfgGK+xpJSOTLjab04YbzktbzE3hxiabKsxGp042Tdh6fnR/d1OEiWNPqY+ZRgXPitF7N43udDceGKPfIxqtp54b/k20YxqeEXtMgF5ch7jzpct35Srxn/1o+Bxn/+gFOgvXVmeefBapZA7Hfd1AXloc9hGWVRWp36c6cDpyX7t7PMnmbC89eisFxdOo3NslZp4WSL1A1/2hEOL/liSpBvxH4O+Af7UdFyOEuApcHfy7JknSca7lZueYAjXv9BHtpzOo2bWhwOh64MllSbz6/eHDW3ruxU0pSbXgmCz0Uhk8Oadf6Y2sSrtJp12bL5dFsi06ydlFBaPCJdm2nfEtRFtPcfkb37r2UtwgUK57Cc8xxzpm+Zvwms5zPEYFDwKpJ59Ff+0HeFtNQsc+oHnfA1jBEO0XvzPsI7z+/Kv5/HxVepswLZCeAh4FfuqeEEJ8T5KkF4H/BBzZ7guTJGkX8CDw2w2mH5ck6QPgCvDPhBAfb/f5P4/oGwY+20IdWP1ZMwiJ1PVm3unMsJn3ZoG0rzs5HU9uDcm6cUvBrpEi+0dOjWk3adC9geN09BRXvvktPIXNA9t2Yx4o57iVWP+CGTpzCrVegS89PJzzFAogK9g+H0JRsb0+hKygFPLDPsJKdg2p36dv3Plq17sF0wLp68CfSZL0l0KICV5FCPFTSZKeBX6wnRclSVIY+BvgvxFCVF3T7wI7hRD1gaL4PwH7NznOnwN/DrBjx46bdjS602Gl0tS+/dLQ2chKpVHGZL1bGIYbKRRhI+eySMLGNlIT6tAh0gtUv/XykAYmlcbDpIp3Wr9SvwosL8DyAj5AtTfedjQf2x2sfMcYwuUlWF4iCATZGNNUubcS0+jU24lp1KybHnXTqW5qtj9lftr+3ZH5bn9j96rhtU2hjWf9HU/7vazPh4p5IpXitVIqJt2nRo8VNPMEqkVaI6puv1s97RqPto1tJ3S8D3yFxR9/l3Y0SvgPv6ZiOH/7LS1JuG/h6bTB6kG3A4pCL6nTN1KUn38Rv2k6zmZGGsRGKl2XG9o2K11n+XPfbpXtZ/WoSVupHSVJygAP4eQk3QFtdLuDwGNCiH9/0xfkCJq+D7wqhPhfrmP788DDQojNe2QBX/7yQ+KtX/3quq5hWm5lK4tA98Ps3nYyZ+Sad527PyXHtFW3FzWXRcpd6zE60VnGda51x6O+ywnpRjEtkE5sv0EgXaeyLElBti3yz36brpGeObc8D6QO5oH0Gq4nkIaKeQ699RMk1Ul5nHziWRqasWkgXVd1yx4V2epz9unnaSaN6wik4+VdxunjJD58F9vnI3jhHPXHn6B89GsAePNZIhVzfH9VGT637i/AXldSVJ2wI3TNT7WFHN/ffRfv9EAaCQaG/5Yk6R0hxMNbbH5d2HJFKoRYY7DalCTpHwsh/s0mm54H/glwU4FUcu7q/w4c3yyIDoJ7VgghJEl6BMc50txo2y8ClFwWNZ+n71LpqbkskR9+D1t2GktXvvUiks2WgXJdzXsnYZ3K6hqOIMlTKAxXpXPMcasRKpuOSnvEbrKhTVKmQTNPsFjAXy0hZJmmniJYyBFwqbqvF92kgbdSJnLyY5Ak5HCY5v6DdI20szIdiPI8+Szaj7+Px+sZPudk7l4zhzsVszgb/fWAxv0vhRDF9Q8lSToC/D/ATuC/vsnr+SqOCvgjSZLeH3z2z4EVACHE/wb8CfCPJUnqAy3g74tbXER4JzHCo4XXSi5L4AevIEZVeoO8ppLPg6JgpRzhgf/USXynTyE36sjVKpWX/5j2PbOltqepTWeFezUkrU2uiNWFDL4PwFPMI8mC9kIG2XtnG3LNWlY0qYydcfsJdeuIEnbGFaJ7hdl2jTuuVWLLpT51ryJbXWvL8ejxutbWK1D3sW8WE8YY7uYBikxLiRBvduHyFeq2zUU1Qq3aGTP/D5cKHPrdz7BlmUCtCghky6ZjW2QDMRrNHpZ//G/W7/aRdz1bdU0nf88D0KzTWNlDoN9DzuXoDYK4NVjR+nJ5bFmhazjaBimXnzmQzroqnHUFejOrzpslc24XFzTLG+lbOCvODyRJ+odCiF9IkvRPgL8EjuNQwDcFIcRbTPnZhRB/Dfz1zZ7rboCSzyFUdUyl1x0EUsswwLomPFJKRbxnT6OWS2DZxF75222jcLcDai5LZOABjG1Tfv7F4Qq5/PyLyPncHXW9c3w+ECsXiFSK1GIalbg+9nm8VqQaS1KNb670riV0Pnj0m8RrxU09k8PlArYsUx8o5IuLK/S05NDj2ThzAimTnnllWtt3gMiFMyidNkhiQ1V7b134l10D26avG3Pf188A133PhRCvSZL0AI5hwusD1ewDwF8B/92gxvQLB2nNafcjbkFfvWmwjBTeft8Jli6VXn8gPJLzeQAiP3sN35lTKCWT7v5DWLGYs/q7QwLTqAfwump4/dr6qTT23B1oji2wUcCMlQt8+fc/x5ZlZNvm3a98nUpcH36OMvj8kW9MDaZbBcF6XEe2bcJmDtm2KezcRzeVJlTMc/Ct1xCygv8knHnquZmC6boi3WcWkNPp4ZfkUfSMNIXnXiRSLg6/aM4D6e3HTPdcCJGTJOl/Bp7CKU15B/iXX+QgqrzyXYSigGXRf/k7cBvzd1YqTfWFl8dzpCM0Xz+VRhhpfJ8cw4olqH39GSI/f51+LI4Ihm+4bOVWoK8bYNtj36zn+GIiOjD9L0e1LQPcOjYLmJFKEVuWqSQMYiWmmW+qAAAgAElEQVRHeTv6eW3webRiXtd5NkM9oXPiq88QKps04knqmoEXCJbMYTs/X8W8oXxpR0/R0VMTfWVH0TPStBcXb/j657h5XHcglSRJAf4ljoH9q8D/Bfxr4H1Jkv7BgJa9K7FZm1xpkIdcb/cj5fIzB1J3DsCtmnSfeyLdkEnTzzjnVGCixEUAGCkU28L2+2k9/lU6u/ZgxRMosoTYIgkhT8kwTEt9TMtv2KMNhRcWaL907UuBZ1BSM/w57qRENVs7TE0rN5imnnZbUbkdf6blPdsjucTOlBxn2zVudPtjY3dOs94en2+65zvj893++Lx7+9G8Z7dvk6iYHP7gDWxZJtK3eetLXxv2khWbqHLV1cuYzR7FmI5WL9C4cJlL/QANEcCotbEbq1Rtm9MEKZVbtAmSarShfYWabXOaEKVya0KJO5oHDbjy8u5tO/44ZOKDH7JHxK9SDMXJdPt4c2v0ZChFEsP76c7H9lzPrSW27ghxM65N07QO7jPPmqd050S3U7R+5+jfxzHLivRtHCr3nwkh/jWAJEm/wMmb/lySpP9RCPEX23+Jdy7EIA8prV0Fy0Lcoe1+HJr3ZaR8DiQI/u43qOUSvjOnqH37pTuG3rVS6bkTyxccsZqzWizGdOKlAvFqccOm7ImqSbxWpBzRKEc0ZGGjVQrIwqYc0QAoRZO89aWvEa8WndXtoLl6KZbk7QeeQmuUqEQ0SjfZdH0z1DWDT446K1Uy6Q3VvnPcHZglkEZxakXX1bTr5THPSZL0T4H/Acfk/gsDkclgvfwdxGiO9DOsV9wK/VQaO5XC9/ExUEZsBPN3Tp50jjkqEQ3ZdoKiZNuUo9rENomqyRMfvoktycjC5q37v8Zb93+NlavncWvsS9HkMBCPkqOlWBJFlojVisPxZohVTFLNyoRg6XpQ1wzqmkHYP89c3s2Y5bf7kBCiudGEEOJfSZI0YSP4RYDIZLC36JfnpmqnwU2rCMlN1br7mbodzjfvdyoJCZFKoViW42BkWc54cI6JQutp1K2LaPmMWgFuiO2mgt1U7uh9d393mnZqy7XFZG/U8e3dVK6bjm26SlBGS1Lcc27q1U3VlpvjcofJ7cfna679Oy7qtt9zj10lLiM/i7AFZQJUdjyCVi9jhmKYvQCY46+d1NU1mi0LMxonWTPxrWYphuOkL57FlmXSF8/xxj1PjAVHrVZEb1YoRRIUIxparchDx3+JLSnIwuKXR75G1ZW/bKkyiYrJkQ/ewOv1INs2v33oacqxJEHveM7STdXOai4xKyabEVz7t/s5nDaelXqdfE/MRuXeytfEdpfoXS9mUe1uGERH5t/fan6OOwMbCpTmmOMOQjGiUYxom+YBS+E4sm2TrJkotk0xHEerl7FlGTOSJFkz2ZW7QLJZphhOAPDUx2+BoiALmzePPEmiVsKWFMxokmTVJFErDQPpOm1cj+tDqrkU10mUC0SrJuVbRAXP8fnFnG/4AmKei5zjRhAtF9ByWSqxJJXPMJiYEY1fHP4qyUaFYjhOcZATXQ+ukWade5onqIeiyLbNBWPZCYbRJDvyl7jv7IdcSu1AFhbJqoksLEoRJ+CO0saqJPh4z/3Itk2iXEC2baob5Gs3QvrcSYzVc+SXdpPdfXDT7YJmnkCxgJJJ05o3Qvjc4osTSKVrlMbtVIBOqm5ddKiL5ps2r7iP6KJyJeGmgkf2nepAsvX8dI/NO4fbnVXVuJV/MoDsuq+2NLKBW6Xr+mCyZ+fWSlo3HTs53nr76gj9WnFRtW7qttLqbjlfH4wTVZMjH75Jz5JID1Z1xYhGz63SdY1tV27DclOcAx5bb5TQmmWKwTiFUGJsm/W5cigxnGsS4nIo7Nz7aocGIV7d+Qhas0I8UGWlfAXTG0OvF+m2+tjtLouNc+y7ehqr1ydSKfLunvuREBTDCYq+GGqnT9gs0LXAjCZIN0tYlsWbR54k1a44wqRAHLoWquthGKVqly58yte/+39gyQpHbIuf/umf07rnXtwImnn2vvEqQlYIHMdpSj8IptN70m4+735OJ8au65ikft3voK3nt5PKvZPeIbPgixNI55hjjhtGvFbCkhXMUGJIha6vBG8WeqPEM6d/jSXJKMLm9X2PDwPm6JyK4Kcjc26YYQ0zrJGsF9lVvIReL6LYFueMFc4ZK3x59TgAF4wV9JqJhOD0wt6xY5QiCWdlWzWRFShHNErRJM3rWC1Gy07966EPfo2v1SC/tItQuYh++RyXNgikgWIBISs09BS+SgF/sTBflX5OMQ+kc8wxx1SUIwkUe50KtYdUqBvJehGtUaYYimOGpwdavVHiwdWPCfTanNOWMepFtGZ5GCy1ZhlLksmHNdL1EnvNi8OVq7lJIDfDGj87cBS9XRm7jg93HUE7XmFn/iLhdoNPNmijXIxo/PI+J4daT+oblt5shGi5wIO/+xnedpODx35HrGwSrhRpROOAhHH2BBLQiF9rxdbSdKfvaCGHLENbu7VN6ee4dZgH0rscSi6Lks9hGal5XnSOG0YpmuSX93+NiGkOla9uaLUiT558G0tWUGyLnx08Sj6wccAFSDZKfOP0rwl029ybPwNAy+OnGIwPtykG4yjCxqgXiXbq3LtWp+YLI2Pz0wNHMUdWp/uyZ9lZXOWCtsTp9J6JkhYzovHByr0889Eb1AMh7r9wjNJIjnV4zoHYyesbfz0mKuagXEYi5JXHcsWRiokty/Q9XpqROLndh4iaOfpeL1p+lT2/f521fffQDYQ48cQfQXCRZtLgzFPPzXOkdwHmgXQDuHn6afm20RyB7c4IuPZ15xMmDu1OYLgdT6bkTEdzqko2S+CHr4CigtWn+cLLWOn0yLZbw30fJmTzU/bfzl6D0xr8uPuCuHsoTnMbmgZ33nO0RMVdvtLtj4871mw5zmklK1XXuFjfPM9ZbHTG5kzXtu3WeE6003KVs4zMl/HT82SgDbQbAGM50nThKvWGRT4UxWiU8K6uUYmPv2LsfhejVSbZqpJo12i1ulwIanTDbS7JYf5gHCTflaFbQZIVLuLh7chOdlWu0JYCLDdMqmoEv2UTKRa4IocBOFA4z5+9/7f0JRlV2Pzbr/wJlWiSZLOMGYxjDtS7Vs/iStSgENZIt0usXDlHPFikGI5TcwUye5D3TFRNDpiXOHDhOL5uiwPnj3Nh3xGqcZ3fP/w0lbhOLZZEtm3UXhfZsmjFNbz9DkKW8fa7SIqK8PuRPSrxWpGusgwMzFJSacJedczJy92v1ONKmrp7jo7+vbv/9t3jiRwn45iWY52GWd8r24nPKsU6D6R3MeRCDhQVK5NBWVtDLuTGAukcc2wnzEAMFQujUULFwgzGMJplkq0KZiBGPhjHaJV5/sIfsCSFaKc+fOm2PD7+kDlIPhAfO6bRLPNw7lMCvTYP508jkFiprnEisYIZjA2321VapS/JrMbSLFWy3Hf1JP4sw8D6+v6jVBJJiqE4im2h14tEuw3ubZ6gGoyg2Da/+tLTE6vTRNXkud/9iOXyGnophy0rhJs1lq6epxMIEa06/r3VuM57j3yDSMXkkweOku5UCdSraNlVEtkreBQJpdfF02kTqJRQzDytG+hTOsediXkgvYth6ymw+ihra2D1nfEcX2is05PbbY2nN0okWxV+nzmEJBgGuWfP/25oJv/arkdItKpYkkJuQN+ejxgU/VHMQHQiiAIkWxUsSaareGh5/JyJL+G1+nyQ2kchOBAkNUsABLttlipZVGFT9YdRe00KYY1d5iUevHyMjzz3OfnTg0fRGmX0XoPl0uqw9nQjAdXK2nn2XDmL7fWSKq5RDUXpqx4kIQg2alRHnJeqg4AKEFk7Qzm1SGF5N9qVC9QPHaYdjZM58RGJ1YsE1y5y7unn58H0LsEXMpC6l/+zlsNsZmK/Edy0iLusYoJmcV2M27jIfXa309HY8RYydF76zjBHKqW3brE0K1U7vaHv1vOz3PcJytwF932b1gJ6WrmLm651ea+Pzc9evuKibl1uQGWXe5C7hMVNz25F3zYa1/6tVYs89s7PsWQZxbb5xeEnKCuRsX07E1SvM9abJfRWhazkIR+4thK0ui2MVoUnL3+AJUvI/R4/XLqfvFA5XF6l3ayS9UdJt6sEr37KqjfEA40S8WYFS9gci6+QUwLQ7SH3i2PnVrwBspKK1G2h9jsE2g0i9SJmIMbJQJJ+z0Jvlvjmud9iywqntB1cDut8lDlEMRjj+Yu/Y1fhEoezp0FIGCff5mcHjw7VvfV+jZ3Fy+j1IrIQlGMJpJGHQFFlFEVClqAfCFJMLtDxeqmFExAI8M5Xn6Olp/ECgUF3lsigc43fr+KTBB6rS8dIYz70mKPSjSfo6SmUSoFYxcQeMEQ+lwm+x/Vw+d3zLqp3lAl2l8ZMczK62XKXW0nlfl6qYb6QgfSLBDudHj6sc3yxkaiVsEbcf7R6mSux8UC6UT2n3izx3CBY0Wnx45WHxoKp3q5hyRK5QAy9bnKgchW9XUNIEO82WWiWaKk+TH+EnDfEDxfuQ+/UKPgi5P3R4XGMdnW4nySgFDHIB2L8aPlB9leuEOt3sV1vVr1VwZYVcsEEiipzLHOQT/VdALy+/ygPXjoGSJxLLpPplNEaZQC0Rpl60uCNe55Aq5cohhPUNhBQXVzYzdmlvcREj54i4++0afv8tOM6tdi17SOlAplLp1k59THNcJSQKnHp3gcBR6nrHaw8Z1HpevM5fGbeaei9Y+s2aY6oMI9lGLBwe/sizzEPpHPM8YVBKZJAcVnrjSJZL/LUmWv1nD/Z+zircngsWO2ql3h47QR/yBwiH4hhtCokOnViHcdBNNZrES9douwNEO+2CPU72NK4rUjOHyHndwJ4ul0l2a6BJPFY8QKBfocHypf5IL5Mp3KZHy0/SD4QQ29XuRJKkgvGSQ3yriWWKARiyLZFqllCUZw87TrMUIL3dhwheeptjHoRRXH4m28MlMXe7EneuOeJYS3pqNhneM+iSV577NvcU7zMQ++/ga/bxVZUWrI87G8aKxe4//03iRTz6NlLnHjwq9g4IqzsnkMAaDCTStebz5F+/Qcgq2D3ab34Mr1NWjSquSzhV78Pqgr9Pt2XvjPXQtxmzAPpdWAWFe8ElesiPmS3+blrf/f2ygR1O76927RempGmHru2m3U+mnJ8N9261fGm0b5uFa/72G5TcPfhphnDT1PiNrcwhp9G3dZdPT+LjXGqdpK6dc+PU7nV2vi43bhGz7ab46rbXOrLQ/FPoe2j06oN5xfMKzTqDXKBGKlWDf/lMzQCCS6169xXLbBcXOVw8QLd6BLfKK3y28QKj5hnsSSJfq/NSW8UWw2zp1UmqwiMepEu8F5skXSnTrRwicuxheH5Up06f5o9RqDfJdLvshZK0FZUesKmLQR920ZrmGQ9AXKeAIqwSTXLKMIeBsxCMMGrux9lf+kSHq+KJEtIgz9kRZUpx5L8/NBX0ZoV6lqSRL0MHpVSJEmmVcZoV6kO6jrd5S7rHVt6/jSW1KKZWiCETaTVROo2IZ0mFvCwmK3i83to7tqNt3CZ5cJlrMwC8kKGWNAJz6H1xtyZDO1MhrBPJThyLnfj7miliNfjoZvK4M2tIRWLtDPXVqWjql2faSKrHqx0BiW7hqeQh8y1VemkindseNMqXTdmoXI/L9TtNMwD6RxzfAGQrBfRmhWuEuTkgPp0wwzEnGDVqqAIm8KAds35o/xw8T4eyZ/FjvY5HTZIt2vsbRSwJImsz1ldmp4gOb+XA60i6U6dlupBCEh36qjY5L2hsfMdbOQ5XMtS8QRIt6sgy6wFYihC4LMtwr0miU4do10l74/y45WHrimAA7Gxl9ee8hVkn4c95VV+snfc/Wg9J+oNOHvIto1eM5EVaVNjCTdqMY2OL0g+tUSwUeOTJ56nltAHc4PSl26H7O5DrB68l86he2jehJCop+tgW3hza2Bb9PXNj2UZhiMqzDqiQsuYiwpvN+aB9HMOOZtFzuewjdQ8FzrHhkjWi3zj07exZYUj7S4/2fPYhjZ7+WCcHy0/iN6uIpDQ21X6kkLOHyXnj/I7Yw9aq0y6XUPB5kxI55F2lXSnhiIEBV+InOLje/pBjG5jGDgPNvIbXpcQ4Ld6Q6HYb7WdnA0b/Nw4gNZp8HAzx+56gQdLF3kvscK51H5OaCsTx1mnns2QhtEYd0baCOeTTg3nlZV9121zWInrvPuVrxOpFJ3c6MK1lXUtoXPiq04D70Y8SV0zhivRG0XPSFN49gU8hQI9Xce3hZlKP5Wm8cLLQ1GhMn8P3HbMAynbq+KdlVmdNH4fH09Qw4OLk7NZlBPHUd55B5FIgGXReellpG18iKZRtduN0fs+TUXr/h1N6+npnp+gcu3NqVtnvLky122YUOtubiIPkwYKpou6zVXbY+OKa/uW21Sh6RqPUruNtkPZNnvkgmGSjRKBK2epJ3YA0G1WSLVrQ/HPBSERquX547VjVDx+6kLie8YBct4wF4G/DWXQe00KniBZPFwOLlwbd3tAj1VgVQ2BDRmrzd5aFkuS2FvL8oP0YXJex0ShoHiRhSDUb2NJCmfDKT4ZUL/3VK5QscJ0ZQ/3FM4QtHoc6jV4dedXyA9KZ9QBHVqOaqh5QbpTIdZvYVhNqr0a9fi1VVyyXuSAeYXDl05QD0SQhU3BfxBf4NorMB72jt3HePDaOBbwQGiR5tIiChB3BUpvaoneyhJenHxoyEXVht20sXd8HHH1Nw16FFhchMVFPIBXHX8PqOObI2XS2Jk0EpPU7aSKd3tVutOo3LuFvt0K80D6OYSczeL93itIa1dRzp2j+8wfIbXbzsp0/m10DhfMQAzZtkk1SzBC2QKk2jW+ffWjocDo7VCaP177mB3tMomejzOeCEa3OQx+WW+I7AhFuz5Odxvc28g7AXVkXu81sSSJNW+YTLfOwUYBo9sk7w0iAb+N76Ajq/jsPiCGQR0kFFuwq5lHAOcjKYKSTLJVGQbSdRSCCX6y9zEON9a4b+1TdpSucOTqp5zYdYjzxk4Anj7+K9LtCsvmFX578Cv4el3iteJ1e+nOMcdWmAfSzyGkfA4UBbF3H5w7h3LmNHZmAXueG7mr4TScLrEmh2fqvJIPxnlt1yMkWxXWhDReutKpYUnysNZzb71ARfWRUHyErQ5xWSXvDZLq1jG6TbKyZxgo092Go7gFjtauDoPxK9reYXDd1yxxqGES6XeI9zscbpZY9UVpqR5+HVtGEYJkt0FL8QISL6x9jCVJKELwu4V70To1mooXn9VDkeWhyMholsk0spjBGIVggkIwQUU0qfjDdFQvB/LnCNkddhUuc15fxpZkVvVllopXWMqvUowlKQ/u4Xojb5HJbGvT7oCZw28WaCd1Z3U5x12LeSD9HEIYKbAsaLfp33uE3kMPYR06PF+N3sVIVE2e/PBNLFnhy6USnywf4nxq5023Miv4IijCJt2uogibM+E0Rr/J+UCChXaND8Np9G6TxyuX6SMj2z2+l9wHwEvmaSwBy50qFcXHqaBGpttA7zmlMP9F7jhH2iZ+q0/Q6oEkERA2XmFzzh8n2WsS7ndIdJuUvAKtW3fES4OgLgFvZw5T9EXYU81yKbXXsRlslnnuwu+RfD5k2+Ynex+jEExgBuOowiZTuoK336Wnegh0WwDIwsbT63A2s4fjy4c4n9lFI5oca+QdXj3Bbx96eluCacDMsfPnryIUGcmyKTz3Au25s9hdi3kg3QDTcqZblcPMnPOcaAI9fX+RydB9+WXkfB7bMBDpjJMbYbq5++2EuyRl0jjePX/tg2nlLK5+0fQncp7j8+5m2u2pbkRbz4+WsJRbs+VAi67ylULVVb7icjJq1joY2SvUmxYdVeGRi6eQqjXSF87w+r7HyTKuhu3WrjkEredAnx7Qt/d2W/wmvgICCr4QF4XEm2qU/U2TU8EkH+HlSnCBQ02Th2gSbZT4e6XL9BEUPAH8Vp9ErQBAr9dlzRMkjEys2yCFhCxJ5GQPRruCv9+mrPoJSj1iVpuSJ0BD9RHpd0nYHbR+h52dKhVPkJ2dKp8IC4+skum1UGWVciLDAn0er17GkhQWS+dQ/X52lVaJSBaXtRR6vciiaFIPpWmEQrwV/Br3XzjGweIF9lZWUWyb9+5/nN/s2k+mXxuzRkyHveyoNgiH/JTjOsFmid1WndXoEgDxwLU8qFs8FAuMj93lK6mrFYJ+D20jjT+fRa+VqC0tbrq9e+z3jCc2va7Ep9f1Yhh1QlJcczdb/vIFSHHeNOaB9HMKkc5gpecOJl8UrJutLxdXkRAUAzH0epE95kUuJw9vue8ofbunVeGP1z7mciCKIgRvBQwer65iSRKPV1fJxVSy3hB6r0nZ42dN8bLYrfNwI4+p+lGFzU+iy+Q9ARQEmV4TBcH7gSQl1cfJkE7W41RIthQPmWaVpW6NgurHI5p8ElmgpAb429Rhkr0mzmta4LP7RLstTkUM4p0mZ6Mp8oE4h4oXh968B1oFvn3qLWr+EPfkzqB6FNreAOZIztSMaFxKLvPhyr2IYABPv4cknNZo7dDk81KNasiWRbxcQFGcUpbtQCepg23jz2fBth13ojnuWswD6RxzfA6wbra+O38Ru9PngasnkRC0PH4+CWSGBu4bYZS+jfXaVFQ/WV+EdKfG/qbp0KneMOluHb3XHOZAd7SrhGUFFYl3QikKHj8+a+DY4wny3fgujtaucqhVwkIiZbU5GdKH86/GVvBLgrwnwG9ji+xulWioXn6u7eGTSJpUp84n0TR6u44sbJabJZ7Kn+KD+DJGt0EtuQMzEEURFqlmmUinQc0f4lzCKV/JxtK8t3xk2CJtHaVwnJY3gKx66MvKlrWilUErtGi1COkM1cT2NNfu6CmufPNb+MwCnaSOMtcv3NWYB9JtwCjVO0vvUrh5qteNaebuN4NZe4JOo3InS1bEyNzW27pN5KdRt7May7vdiGpuN6IR+naaiXzORd02G1uXs7RqG5e3VPFzLnqASqTAY80WF6JpfL0uwdUTNOJLw+17jcrw31a3zSXg78KLGN0m/YiXo7WrJCs5hLA57tc42imhd1qAYM0nSNZy/JF5Cm+vxYIE34/u4GCniiWgJynkFC/CttA7dZ6pXSHRb+NDcM4X4XCnSsp2qOmjzTxtb5hEt86+Tp193TofhjS+2sxTjhrkYmn+RsvwldxpCq0ilj+C6NWxgzEkxcOSbHFS38UvQmGSrQqn/CoPrn7CklWjHw5z4uCDtCLa0CEoEHHKVdrRBX4X+TqL/TqVqIYdSxIHkmHf2H3VQoPyltgOeuwgHvSMkeSjdG7EVb4yjZoNehRYXoLlJfxA0EXVurd39xd1U7kuz/oJU/tROndm6nbG+pR5ucsk5oF0jjk+ZzgVX+KB4jl21tYcM/hkZMvt1xW3eW+QKx5n232tEqcDCY55nLKW/e0yp/xxsp4gT1VXOdIq0ZVlUr0WWjDFd+M7Mfot8mqArCdIutfkT8rn0PptjL5T99qVFNRGjrLq52DTxEbi48QO3gtnEAjeD2c4G3JckfROndzAtP73qX0Yq+8TtnoowsZrdx1z/XUbwFCCQiiBP+SlFIqjNSsUgzEaWwititEkvdDCpvNzzLGdmAfSOeb4HCLc65DoVCn5oltul+rWeSn/KUGrR6zf5mehDA83cgStHns7VexQhqONLBYSRxtZcooXJAiIPkvdDn7L4mgjy9uRDMcC1/KHRr9FRfHSULxErS5tWeVXkQy6sGjLCjs6NXy2xYLo8nE4xWvaXh6vXh66IhV84eGx8v4oP1z6EhlJ8ObSfQCYgSj19e4zg16ndaEP7f4A/Nt9U+eY4wYxD6TXgZtxPpqld6lzrtmoXje2on6n7evGNGN4N9xKWff+0+ja0f3dzkNuVa6bqp2uwp3NSL4ygxLXbSJfdpnIB66sodXLFMNxR/SygSp3FJ1GfWw8qsIFuPfiBywUL1LxBFhoXGSnGqYd0jG6TQQOnbtujBCvZvG1quzs1AhZXf5BJUtIWFz1BtnV75KzBX1JYs0TINNrYvRbnPAnuOgJ4bEtsv4gQlI43KmS80WQVYcOLaKh1rNEsOmrXi6HkpyLLbLUyrOjU6XrC/B2fAcpq8eH+j5Op/bhDcU40K1zNpqhmljGD3gHq8oaGXqhcWehYNDj2Bte+QOWrBBoneONe58clvwEXE5ESddYc1G5yZB7fnwc3YK+dTsT+ZStqVr32O1M5KZm1S1UuLCRW9Hm+7vfAe59585F2487LpBKkvQ88Fc41Rz/Tgjxl655H/AfgIcAE/jPhRDnb/d1zjHHZtAGxgnlgcjl0eNvjTXTvqJsTcXOikSvxUv5Twn0ezxYX+O9QJKG4uEVbS95T5CY1SVkdakrXqCP1ne+BEgSlFUfqX7HUd8KMaRu/33yAP/I/JSdvSZpq8VXmnlOBBLkB4E06w3yTjhFWBacDWj47T4Sgu+nDnOglqclr9L9/9u78+BIrvvA89+XWXeh7gvoi93No6kmJZ6iZImUKInifayvtXZjZrW2N7T2rCdmYndjRw5veBWevzxjz07sjndmPbZjxt7ZsWfG4xVFURIp66AsiSJpSbzZZF/sE3UCBaDuynz7RxbQhSwAhepCA4Xu3ycCJBKZlfnqaPyQv/fe7xkmeV+Qd6M5ss1F7qmcQvnD3FM6TjkQWVUYYt3XsjaPZZiUppLs6VRJLM6NPXdWiK02UYFUKWUCfwB8FjgHvKyUelpr/VbfYb8KzGmtb1BKfQ74XeCXtr+1QgyKV8vc9tr3sEwT07J4P7t/6GLao3o3kuWtSI6g1eF8IMqcN0ii06JtmHSVQdMwsZRBulOnYHh5NZQi02nQUAZ1T4CyJ4CtFGe9YX445UwJ6e//BHgjlOKZ7gE+WStwMhAlYFtkOg2KwUtTTd4Jpri5WyfTrhHrtngpsnjwrvwAACAASURBVIeCf4qCf4p3IxnSrRrzsSyFQISj1QtYyqASjJFtVEk3FzYVSJen/aSXKpi+1au1JBbKxBcqzEeTUupP7KiJCqTAPcBxrfVJAKXUnwNPAf2B9CngS73v/xPwL5RSSk9IJYJha5cOLdgwYup21HTtRoalcscZhevsX328O13bn851r//ZskYrmDCQynUVll9wbVdd6dZRRuL2F4mPXbhIrWFRisRINyo0Flt0a20itTxdbM7ZQRYq9VXncqdu2/Xqqu3+UbgAZztd/jR+eKVYvNVucn27jsdqY3bbeNt12oYXq1XniVqBsN0h3a6x6Iuw6PXzjeg+UFD0BCn0lkBb/r/puZTufC+6h6N0CCmFqU3mImn8fYFsngQ/jkR56sKrLARSfKJTpeH3UwxEWSDDAk7qNgTUgmGCrXn2GRZGMERt5hChkDOAaFnIlWoNhL10knt5Of4ZEotzdGZyEEuRxPmD5cF3X8Q2DIyCzY/v+TTe1OppLu7UrbuIQsyVrg1ukJ4dKJjgGkbrLqDgLoIwmMpdtTm8iIL7+A2KLAwblSup3K03aYF0L3C2b/sc8JH1jtFad5VSVSAFlNwnU0p9AfgCwP79+69Ee4VYZS6SwNA26cUKhrY5lbmOd8J7SdbnqYTizvJerj7V9SwXcL9oaQp9g3NgdfF4Sxt8OXGITKfON2MHsK02RU+QTLeBpRQ+28KLpuINMO/xg2Jl4NBGvxPzvhBfSd2wUvIv3anjaS252qJZ8AZpmSahbsu50wwMDoAqhuJ847oPM61bK/VxN6sSTVKJJolGLvV5xhYq2IZBNZEhNlckWi3T2Cv1bMXOmLRAuta/a/c912aOcX6o9R8Cfwhw5113TcQdq7i6VSJJXt1/lAPlc5xJ7aM8laSpOhuuj7mW/lVZaNZ4JnvzQDDtl/eGVtKydrdNrlMn1Wmyv7XEzc159rTrfLJ7gZemsjwTG1zTc93z9oL1E+XjhK0OiblTfDdxkIovRMkXBqX4UPXCSqH5F/bdvu65iqE41WBw09feSDWaxDhvE5srYtg2C7EU460AKsTlm7RAeg7ov3XcB1xY55hzSikPEAMqCLENYvMlogsVOsbUmv1yycUKt519C1sZ3Hb2LebCcc6r4X2imV6/YSkQ5Tyry/qlWw3S7dqGgbRfrlPnqfn3sZQirLsUPQG6yiBsdwnr7soxmW6Dkm9qJQCvJ92pE7Y6HGxW2d+pc2/lNN9NHqLgn+JkfB+vxfbSMkz8toXq+5s201xgpr1IORgbWPpsXPOxFD++59NEq2UWYikW4mmkl1TslEkLpC8DNyqlDgHngc8B/7XrmKeBzwM/BH4B+NZ294+OuxD4dtqoD3VYn+hWTmeB4VNa+vs1h1Uici+e3RjYv3Ef6ECfqKvakHtKS3WpTWKhzId7K7Ckmh2+e8u9VCJJGn3HzuRnabYsWh4P++dnmTl9nHdTR1ada7lP1Amei7TrVT4ydwYLAxObL8cPcgG4q7lEqlmHdoOLXZvE3EVurpexum3eCSZWAmC2tbhqsNBySnfWGyJmd7mhWaVjejjnC3LRH+FoZ4kjzSpdwNtZ5CupG1buPL2B1QXwPcEploIhUovnyGGxx2qiDcUHujVa0TT+WJqu6oAy6WqL+t4bCYcSpOtzPJh/DcPvw6yd4Zs3foxyOEEgvPq+MdC3eHY4svF0lkxk9czRxFQSOEACSDDYJxrxuRfTdi227dt8taJh01fcfZbj9oG6Ngcev9FYC+kT3X4TFUh7fZ6/AXwDZ/rLn2it31RK/Q7witb6aeCPgT9TSh3HuRP93M61WFxL4otzWIZJJZoi2i6QXBqcilEJx4g2axwpvYFW0PT4eSuYW1n+K9WocrH3F8Yj517FMhS5ufMseIIcn3Kq/mTaNd6M5PhK+giZdo1Oq86Repn7F85xsFlF2zavh5L8P6mbAHiyd/dpas0PwllS3SbxrhPca6aX/5C8nvsXz2NjELc6JLpNQlabpmEStPSq+rprKQQifHnPbfzqqe8ziybabWHYNtF2neOJvRxP7CXVWKAcjFLt9X2m6lWCnSa2qfBbbVK1ecojpreF2C0mKpACaK2fBZ51/ey3+75vAr+43e0S14bofIlotYzliQysSzkfSWDaFsmFMrZtU5kaDAzlqSTvx3LsrV7keOo6Oh4vqYYz6vbB0y9hGwa315c4HslgGYpCMEZwqUKs01ip+lPsBbXlVO6jpRPk2jVuqxUpeEPUlSJkdcl0nLU2l+8+76wV+fXiW86dqNXmhD/Ci9G95L0hyp4APz93gnkzwG31Crc0KiwaHryGyV8nDg59Xd6KzfDHhz7OzxXepovCg+bp/XetTIdZ/v/yPaFWcEvxBHi9mLbF9w/dOfJ7IcRuMXGBVGxsYA3PYfs3WONz1Oks7uPdqdpRC8tvtAboVk9nmXendhvu6S4t4tUyN/7kO1iGSbzR5nsfuo9Krx+0WevQMCI8f/3PkFya46IZpqzCsNRaVWQ+XZvjxvPvkpsvEF+c46eZ67k4dR3p0hna7QaFYIxUt0m3VYNWnVS7wZLWPJ+8AQUUfWEuKBN6C1In6hU6tsVx3xRHa0WyrRrzppez/jBFrzNwx6MUR1oLfLhRxkJxc3uRoifAHa0qrwRuwuMLY9oNlgJRLG+AqcY8709lOBOMEzRN/OE4gaiz6okvvHpup7dv+3RqL39++EOk6tWVkbfR0OCUFYCoHeTkwZvRwRBeq0M0HiSeCQ+kdvvTt6NWIoq7prO4U7UR3yYKy/e33TWFpT996648NKzS0JVM3cLG6dthmVhJ5W49CaRi4viKeczZPO1UhtY2Lj8VW6hgGSZzsTShdp744txKIF1WiSR7Zf7aa57j+spZDiwVKQVjpBpVTkdyK4UHTFuTbVRBa96NTFPxTXH9UoF3/EneiuQunaQXRAFK3hAeIGB3eXkqxwl/lIrhXekjzXXqHPPHONSs8koow5HmPOluE6/WBO0uR+rllbTt7UsFbNNDyGpzLJyhZXjQpndV3dthSqHEpqauzIWdpcxMjxfL3HgpMyF2OwmkYqL4inkyzz1LC4Wyusw+8Ni2BdNqNIlpWySqJbqWtVLibyS9u/KGx8+iP0y1F6SKwRhf23cb6eYiF3s37h+Zc/o2f6ZWoeQLrzkqN+8L8+XEIW5uOAOU3gkmmTWdO7dcp87fLb9L0OpiYLNk+jgWiJOyWs76o50Gdy3Ocizk/DHwk6kMXW8Qn23xaiRHxRtiLppZKcawlcpTSb7zgY8z3a0xF0lIWT9xVZNAus1GHeA7TioXVqdz3alZd+WhwVG7l1+ZCAarEw1L19Y7FtGLszQ1LCTSBIp5uhdnWYomB0bp1oaMynVXJqo22itTVxaiScq+GPFqmdhChWo0yaInwqInQu3Ix4gvztFqWIQKRZr1LpVIkpYrFdxqXLp+uy+t/HZkD29FZgh0W5yPRDkWTtPt3WFeNH1cDKfoNpY4unCRjm2T90dIN+qkW4vkvUGy7SWSjepK0XkAw/Ryc3sJSxl8uFHhlXCWY6EUH22UuXepQMEfxm9bPB3fx/Fggnfa13HrUpGToSRhw2Svz0cpkqTTXkD7AnS15v29RykGovgiyVVrcPpCYdL1uZX07VJ69R8Ty6nZ1FKFRG2eeiC7Kkj2p26tTJjmlI8gThUVGEzf9qdnB4rIB1yViALuUbjuUberE6buUbt+z7A1P9dP37pH6bpTq8MqDw0fOevaP+TxbhvtllTulSeBVEyUViqDsiwCxTzKtmil0lty3th8ibte+TbaMFG2BQdu5ejxV7EME9O2qB35GJVoaiWV+5Fj33HKz9k23z16Lxc9m7trK4US/MfrP06quUA5ECXVXOCT599gwRfipfRhCr2qPyX/lHPX2FpEYVP0hVaWPOtoG1Nrfhh1KvWkmkuErA4+u8sdtQKZdp1fLL3LdHuJmU6dsO5S8QSY8wR4M5xhLpQk220QsLuYhqLkn6Lgj/DV6aNMY1MKRNasPgQ401ZO/ghLGZja5rvB+wZG26aWKtz/9vexlYF/9hgv3Hqf3HGKa5oEUjFRWuksFx54FD2bp5VK00xvTVo3ulBBGybz8TTx+RJ7Zt9f6Q9NVEur+kPji3ME2w06Hi/ebscZXBTffPqzGIxRDMa4ee4s/9Nrf0VuaQ6weal8iudmbuEtX8QJbLkPkG4tMYtBwTfFLUsFuhjM+kLcVK/w88VjnA1E2VevcrRRwaMt9rRrmFpzqLmAB5ua4aGjDM75Iysp3IJ/amXqTH/qtuCPMBfcuD80Va9iKYNiOEGmNrfmtJVEbR5bGZQiKWZaW78iS7hcJDhXwpyZppHavj5yIS6XBNLLsFEBBneR+mGGpWZHTeW606/9xw8bhTusoIJ7/1akcvstF1XQHQurY9HoWDR6Kd31UrlTlSLh+TIVf4zFxKW7V/eo3iV/jAOtDoFinrZtczKzl1vnX2eqlMfSNkV/jE7LuVanY3PTuXexlYmhLX5w6E66vRHFqaU5UvV5Zo3wStk/ba9+Hsvbh+Yv4LEsSv4wsXad2+bOsOTxc9gb4qvTRykE4yjDJFebx9RdKuEkvlqePVabhLaY90cohpLs77Z430wz5wtyX/k0CW1R8zkjdmuml3Iwxiu5owRiGYKBCB5fkEVyLALeUIz+ukX+yOo70YBr1G1Xe5haOklI1TDCHroH9hCPXEr+BsJeLP8epirHCbJENOLBf3gve2POMcNG3sZCq9O1/enbiM8kUCqw7+VvoQ2TwOk3VvWRu0fZugssuPcPW+PTXTRhoMhC37Y7/TlJqVvn8ZvPz0oqd+tJIBUTJVAqsO9bX6OpFcq2OXX/Q+velUxVitz8/W9iGwbpZofXPvqZVcG033wsxYt33r/SJ7rU6HAmsx9QnJk5SMVzKcAoDe/M3EDb48PXvdTXmlqa44H3fkBXGXyw3eH5wx9dVUN3ueDCrFYUgzFORqfpGia5xoLTZxqKcyqSwddskG45i3c/NvsWXW1has2L8QO8F0pjWx1eju7hZxbOkWstUTe91D1e5j1B3prKsq+1SMDu0jJNKt4QpWCcpNXgsdk3+er0LVR8l1/PdnmQUKI2z1w4jh+4/sKJVQOG5qIp/ub2TxBfqKBmpqnGtq44n79cQhsmzUwO/3wJX7m4rSO3hbgcEkjFRFn+RVpPZAiV8gTLpXUDaXi+jG0YLKWymBcvkjt7gumzxwkuLlDyhbmw7zDV+KXAOh9LMR9LEa+Wufe1F7CVgaFtzswcXHXeuUiChi+IrQwn/Rt2ig2k6vN0lUFpKklirkiqUV0JpJn6/ErBBZo1vrbvDt5J7OP3PvgUH7z4FihFql0nYHVR2JT8U6RbS06FIQ2pTo2fnX2Dc8EYhtXlK+HMSnq2FHBSs0dqReKdBrOhGHsaC/wgfh1VX5AbOovkA1FyzQXSrUUqOK9XprnAdLPq1LrdxNqfy8pTScpTSVJLFT7xxvdWXqcXbr2PetiZpjMXTTEXTQ2U8RtXK5VG2b0+ckPTTmW29PxCXAkSSMVEWf5FGirlUbZNY4PBRrV4CsO2mSoXUEsL3PTaj8ieO0miPEsxnuXUDbfy/U88sSqYQm8JLmVQiaVJVkvEFytcTFy6I61EVt+VAdxUOIUGPNrmYPks4doip6MzHCmdpt1sc3D+AuFuixPxPVy3VOHDhfd4OXsj7yT28Xqv6k+2uUCquUjB8FLwR0i3lritep4ummS7wbFwGp9l4et2VsoEFvxT5Dp10u0aWsO8N0jL42Oq06LqC3JsKsORygK55gKm1pR6/aGZ5gKPnn8N/GFMbfNy9kbQmkVz76aXMFvuCy1HU6QWyiQW56hP54Y/cAzNdJZzn34Ef7mEZ2Za7kbFriCB9AobebrKkGpDQwvHbzClZdh0llH7SIctvt1ynWDYdr1jUY+laHziQXS+QCOZph5LQddiqbm6z7PRtmhMJWnc82mm5kvYpRJH3nyFtmHS9AVoGSaqXsNXKtAIxVf6WgGaHZt0aZZAo0bLG6ASimO7XpvlwgOppQr3v/MD2pYTRE8m9/HR939KG4Nfeus5TsX2cF3lHKdiezhUvUC40+S6uXMo5SFz4XW+fuAuZnup1oovSCWaw+628QKeVojXU4fwdtvcsJTnQ/USWbuDR9t8L3In/liabHOBxyrv0VWKRKdBWHe4bqGIBjrtBd6PHeVb0wdXat0uBeNMhcIcKJ3GE0sxH89wqHyOny+8zmwkgy9f4Ds3f4zylJOmDbj6MIN9d5iWfw/J+iliagmz1xd64/TqQVej9IHCYLWhqb7FtVf6OKf2w8H9hLwG/Vdz94F6jWHTWVZtjrV4trsP013ZyE36QK8tEkjFFeMr5vGVSrTTadqZzd/JNFJZamssUbaWpUSapUQaO3CRQ8ffxNPt4Gs18AYitP3BVf13iWqZ/RdOceTM29RCU0zVF3jl9rud0bqN7prnTy6PUJ2Kc/TiMfZUztP0BZkLTrFvYRaf3XUK2Qei1HxBbA2vJw9yMj5DdrnPdOpSejLTqJKsVSgFIpQCEUytua16nlRrkbbh4b2pLB3TS7K5xAf0eVLtGl3l1OQFKHmDaNPD6UgWv9Uh3VzkveTelVq3y8qhGKa2ySxVmGovseSfojiVZKZTJVmbXwmkG5mLpnjprk8Rq5apxlJUYylkkosQgySQiivCW8yTeO5ZtGmiLIvig49Sj2/NnNC1LMTT/PD+Jzl1wy2EF6sUvGHO7z28EkgT1TIfe/W7JKtlZkrnePHGe6j1poIkF8qESyUqU4MVeCrhOIa2OXrxGPed/FtK4Tjp2jwvTx/Fo23ahgfTtvDbHeoeP69M38ydZ18jW5/H1Dblvr7JTKPKL556kUCnTtPj5y+uu4dTUyk+WnyPi8E4B2slkp0aRSPKnfNnmfeFiLXrGL07r0SnwclQCtVY4OBigbrpX+k/dSuFEjx3+CPMWDVe5Qh3XHibzFIFw6eohDe/NuhyABVCrE8C6SYMm9EyypSXYalcd7p11FTuRunaYalad1sGKhdZG6dym31riJqzBSxl0Epn8RfyGIUCHVeQ6l9zNFAqECk46dxGKkPbtR6pe9u9Xqlla2cAzFHnl/78ci3c3nNIL1YItBq0TS++dou9pXPMRZxj73vte7RtnAIEtzjFBYxeXnAunuaFW+7lgb99ntl4llPpA3RKZyhGU3zl9s+iNHTaFkpBORijFE4wH0msVAZaCCXw99p6dOkit9ZLVP0hYvUKb9otGsn91IrvsuALM2t6OJm7kXOxPRxczDMfSuCrz3Em7hRmyBWPcwM2t7YrnI3ksEMRptI5rOTqPk9/0Pln3UmFKPRSry8f2OP0cWYzWNEUy6E0HV09XWXUwvFRv6vakH/za3w628bAPk8hj6dURGVzdLOXMhme1Q9dYzrL5aduYeP0rTtV6zZs+svg8ePlXyV9O1kkkIoropNOg93FX8iD3aW1wejLQKnAgW9/Hb24hHepysnPPsHS/hu3uEWKG84cwzZNlIYTM4d58/CHnDVGTZPyVHxlQI37rrQcSfLi4Tu449ybHJk9QdcwefHwnbyXOeQ8V9ec1fUKu6uV/1zaOJ7Yx9uJ/QS7LS6Gk3z7wN0ow+Rw9SLZ+hyGbXM8uZ9Uvcq8L4LP6lDzBDgfy9E2nSXaqgwf2bpcbD/g6sOcNJ5CntjXnkGbBh7bZvHRJ1cFUyEmkQRScUW0MznyDzyGv1yklcrQzmTBVYBhWaBSwlOvEbhwBl+9xvXPP0P5qb9DbUunPmiO7z9Cx+vD22lzPrN/pZKRaVmkFsqY2l53lZK5cJwTmeuI16vMh2JUQptPjy57L7GfdxIHCHabXAilOJ7YRzEU5y9v/CSpRm+aSsgp0vDcwXtWflbpBWUPFj7LGYzk63awDHNV6vhq4CkV0aZBNzeNWShgFosSSMXEk0C6hhGLE61+rGvbnS4ddvxWpnKd4ze3z73fU8hj5gt005mVX2Tu9UTdqd6B1G8qcykY2nqlElLs3beInD6Jsfc65m46Sj2RwrO4gKdeox0K04xE8VeKWFoTmitRT6SpbnLKxjJ3gfJ6Ik03FMI2TLpeD4vJNJnGPPFGlbduug2rZaGV04/p8RgUXIN3pjs1SulpjkVuIbVYZkYvUQs7UzM8vtXXslyjmXXveTeiM3wt8kiv7F6cRjjBFNBKTnGhd2wUMAxFmwgX2Q9A3GvQJcyLqRDJ2jxveD6O0lCZitONJEkEXcXZ+wrBu+d5bnXqdljh+IE1Pz3uNT8vbXtMMGdy+LDxlgp4sOjOZDG8zm28OxU7kMq9gmt+XunUraRqdzcJpGKAp5An+rWvYGGAbTP/8ONbdlcQe/ctPvBH/yfaNJnpWLz2y3+PuZuOcvqzj7Pv60/TisboBoKA4sbvPbdSZL724U+zlBzvDvVs7gAKxdk9h6Bjce9PX8AyDEzb5qf7j/LB06+vlAX89s33rkrxVqbimLZNarGMadsr80vBKeKerFWphGNDR8OWw4mB2rUbSS1VyLYXqITjK4USPK7gdDWxsjmWHnsSs1jEyGaxcnI3KiafBFIxwCwV0YZJJ5PDm5/FU9q69Frk9Em0aVLbdx3+s6eJvn+SuZuOMnfTUZqWJvb+SarXHYZWB22Y1FJZEmdOcOCNv+XMrXddVjCNzZf44E++s7LSy9k9h4gvVLCMS0UZ9hfOEmg16ZhevFaHg7OnSSzOrZTGc4o03EtyaZ7KVJxyL7WbWqrwiWM/WDn3t458jEJg/UCZWikEHx8aUFNLFT797g/A48HQ9qr5n1czK5vDyuYGBhMJMakkkF4G9yhdvWrf6mNHLbgw6pqg7sLxo6R23Sns5dSsTqQJdC3U7EUs26KZTNGx7YHU7eCoX/e1B/PaiwcPoyyL8Ln3sbs2C9cdBiBYKrDntVfQhkn4tVc4efMdeLRN6twJcu+9SfeQTeSH87zz8QdYSmYGUreWvf5d2qHCGXK1CvncAXydNntaVfKZLKGzbxGoVzBMKKSSHH37b7AMg2CrQaRVo5jMYcza/M2HPkEpkqARmeY80yQXytw6f5a5SIKEXcMbCrDQq/6zTzVpJp0CDMnFyqpgnFys8MnjrzhLlC1cGiE8sLalx9k+2L5IIBpkPpkhWS1xazvPQrtJK5plvm9KSsS1TmesrxD9sIIJieDq7XFTt6MWju9Pxw6MsnWPot1gvdC19o9bOH6cNT7dJHV7dZNAKgZ0sznmH34cCnm66QydLRzsUb3pKG//d3+fyOmTFHt9pOAMONKGST2dJVQqAJr37nuQPa+9DFpRmjnIVLlAeL480l1pdL7EoeNvkMufJzd7nrPX3cBCNMl8KLGqiH1ortQbjOQlV7qIVmpVCcHlmrrJhTL3vfY9OigM2+b1Q7diaJvUQhmjb7BScrHCJ9/83qV1PW+5j8TiHJar5N5Gy4/NRRIY2iJZLTHVWOTmM++wFIoQOPsWP7zj/lXBVAixcySQCmBwcFE3m6OTvjIFw6s3HaV609FVy6g1k8s1dgso26LRW8WlGY2TuHCGqXIBw7apxQeDx9RciXixwGIsNbD6S7Rapj4V5bUP/Qy5/FmOHzrq1N5tWytF7AE6XZtmIIhtGMxHk3Rtm2S1hKFt5vuC3cp0mXCC1EIZpeGFW+9bdeeJ1msGzblIArMXdDcaIbysEk3yvVs/Qao5z97CWa6/cIJyLI2XLrGFigRSISaEBFJxRQcXAfhLBfzlIovx1LoLdTfSWU7d/zDBSolGMg2tLjd+7znsXu6vsmc/petuHLgbnZorcesPn6epFYZl8+pHVi+lthBzCtv7rDbVWJoLew+vef25WIof3v5JYosVqpEkrY7FgYuncY+rno8kVqbLGLYTDCvh5MCd5VpBsxJJrtyZ9i9LtpFKNInpNbjn7R+xp3iBPaXznD1wE9Xo1d9XKsRuIYGUra1cNPhY17UGrr3xlJSBPtNhi3NvMKVloL+1d6yZL2Bh0Mg6g4so5OmkMwPPe3CbofylAnu+6ZQKjHa6nP/MIyvB1N0n1kxnafX2Rd9+A8PjoZHO4lEGdjqNNT3N8kqby/1h2cY8kU4T0/Ti6XaYbs5DYBrfch9qcIbjn3jICeSxFGYiTRKYCqxROSm6lzp78QLRUp5b372IbZrc+u4sL951v1MqL7GPt+MPEp4vsRBN4YmlSK/1QqRDvJF8cCV1bMZSTtmEdIiasR8fMN071N2PGHT1Sx46nyc4neHM/n1kZs/QuO0uMjcdXCnDMNhHeqnfc9zpKxHXfnfftLtQ/OAUFVbv36D60LDpKwN9ya5+x61ePFsKxYvNkkAq6KYzYNt487Mo23K2t4i/XESbzkLNZn4Wf7m07l1pv0Yv1RvupXrr6yzYrYHp42/RwcCwLd6762MDxywm0pQ3cffXL7pQwTZN5uNp4vOllcLt4NSfHfV841js3VV7Oy0WEhnyB27YtmsLIYaTQCqu6OCiViqDspyFmruWRWuD9UX71VMZTnzyoZVUb22dwKWAizfeQtPw4Ol0Vu4qInMlpubLLMUH+003YyGaxLAs4vMlDMsauXB7vFrmoz/+DrZhYNg2L955+YODFuJpfnLPp4lUyyzGUtiX8XyEEFfONRlIx6lcBBtXL3Knat2GTXcZTPUOK3K/+gdmPo9ZLGJlnLtKs1jA6g0gcqd9+ysVddIZ7OUg1zun+/hh3Kkwr2lg56YpPvg4vnKRxXgSK53Fi5PyjRWLtFLpNe9QTQVMT9OcnkYBU9Y6RexzOYxIBL/h9JF698ywv1Xl0E++7RRzOGVx7N4HmXMtyzaY5nZtRw5wLv4oU/MlluJppmIppkZ4LWaWzpOMhlhIZohWitxiNrmYcc7gTo+6051B15qdPo8BuSngICGGF4YP9m1vVCQeRk/dDhaGX7W5xvQW15SUgcLw4I4InAAAGA1JREFUm68eNCx167aV1YgkdSs2ck0G0quVWcgTfvZptOnBnJ8DNJ1YAmVbLDzyBJ1Ur6Rdb3UNkqktvftcTyuTdb66zihdf6nAnr/+Gl1loCyL0h0fBg0LseSm0r5ulf2HsLWmcvBGaqkM6eNvow2TpVSWqXKB0Fx5IJBuxvJap8DmOoT7HxtPYdgW0UoRw7ZYWmO0sRDi6iCB9CpiFoto00M3N43v+LuoWo32PTPQbGKWipDK4inkiX/9GTAMglaXuYce35Zg2s9fLoFh0EzniJw6zv5vPE19Zh/xTpczn3p408E0VC5ywwvPoQ0DLIvKQWfFmEbC6V+dKi/3r25vEFtOK586eidofdnpZSHE7iCBdA3jjNJ1GzZK132pgVTvwONdx/dtd9IZfFYX3/FjeN8/hVYG4W8/T/MDt9JJpbG1xigWsA2DTm4ac/YinlJx04F0IHXrHlY5zPKCktkcXjSRcoHgUpVOLI6Vm8aTnyW+MEd1ZmYgReh3LUbZ8dok6vMEAl4a6RyB4iy5+jxz+/bAvj0UH3qcYLlEI5UmmMriH1gMYOP3eK2qTMtC5eJK323dtUJNqFzkxjdewDY9GFaXk/c/zFQ6uzJCF9ZKgbtfV2PD/X5z84Xh3ftGTd0OpGpHrDY0SvWgrR516ybViMSVIoH0KmJlcyw++gTBF3+ABqxMFs+JE9Rvu9OZF2ppuukMyrbw5mfRWzxCd7NamSyzDzyGUcyjb7uL9I9fIlDMY9v2pgcjgVPEwbBsgqU8WDbNvsc2UlkaqdHTxMOEykWu/+43Vorpn/jkQ6uCabBSwjY9KxWagpXSypQeIcTVSQLpVchKJFHvn0I1m3Rz07SO3Lyyr5vNMffQ43hKRdqp9GWndb1FZ1BTJ52mkxn9HK1Mlk4yjb9UYPHQ9aBh7vBNI/WRNtJZ3v/UQ8ROvjt0kNdWCfZKGdbSWcK9QNkfSBvJNIbVJVQqYFhdp7iEEOKqNjGBVCn1T4EngDZwAvhlrfX8GsedBhYBC+hqre/eznYOM+KYlNGPZ/3UsKeQJ/zsV9CGiQZa1x1m6YYjdNO5VTnj5RKA7vSmv1hwVnpZngJjrN04bzFP8rln0KaJsiwqDz9OJ5MbSJ3Zrsd7XddT5SK5b3995e6ufeQDeHsjVi3tSuW6Ru3a2klR+v0epi+8D4bBzMUzXPjMI7TS2YHi/m6Xm74P7N9D9N1XiS5VMHwGtQN78UUClw6I7Gcp8iT+col6Kk0snR14XdzpUHf61Gu61+x0p7nXX9MTwOdRffu2N3U7apGEjY51k9StmFSj9nJdSc8Dt2qtPwS8C/zmBsd+Smt9+6QF0Z1mFp3lz7q5aaxYgm4qtelSf95CnsQ3nmHqJ6+Q+MYzeAv5dY/1lJwiC53sNNo0nRHAl8FXdtrbyubQhom/PPp5VgYuZXJgGM72FdRMZzn/mUeofOiuVVWa+rXSWRaOHJWUrhDXiIkJpFrr57TW3d7mi8C+nWzPbmRlnP5PT69CkTVC/6dneQ3S3DTa2Dg4dtNOkQVvYRZlXX4/azvltNdfyKNsi1Zq9PO0UmmwbQLFPIzYx3q5muks1SNHL2uqjhDi6jMxqV2XXwH+Yp19GnhOKaWB/1tr/YfrnUQp9QXgCwD79+/f8kZOmm42x8IjT2CWiitFGIbmOJcf2zcIaViZwE4mR+Xhxy+lgS+jjxSgncmS/+xj+MpF2qkM7csIyK10lgufeQR/uUQrlZa7QCHEtlPbNUgDQCn1TVg1E2DZb2mtv9w75reAu4Gf02s0Tim1R2t9QSmVxUkH/32t9QvDrn3nnXfpv/n+9zfVzmH9ZxtVNnJPm3Af697f2aDIPEB34PiNi9z3P95TyKMKl5ZGGyiI77rWcqGG5ePHNWyKyeBC4Gvv6x/Y1F4naI/a1zzMsP46d3H21Y9df/Hqtfa7+zjdx29U6N15/O5ZLNttlG7KUftAB64lfaICCAYujWlQSv3tVnQRbusdqdb6gY32K6U+DzwOfGatINo7x4Xe/wtKqb8C7gGGBtJrjaeQJ/LsV7ANA2XZVB95HGWzYaBcHoQ0SbzFPOnnvoqlTAzbovjgo+sGUyGE2AkTk9pVSj0M/CPgk1rr+jrHhAFDa73Y+/5B4He2sZkTxyzk8RSLdDMZrL4gaBaLYJp0szk8+Vn8776D7/hxjNoS5sICc0/8LPUP3LKDLd8cb6kEhkk7k8NXyOMtlSSQCiEmysQEUuBfAH7g+V566EWt9a8ppfYAf6S1fhTIAX/V2+8B/l+t9devdMO2L/k9nNGXDDMLeYJffRrt8aC6XRYeexIr4/QRWpkMWBbefB5l2xgoPPUlfGffx1haIvnMf0ZnR0vhjptac9sotdxKO+3yzEzjfxX8lSIY0N4zg8fvXet0Y3GnU91GKWhuuBKWA/sH0qEbP97dNndLxlnjc6dTt+N8piRVKybFxARSrfWaiyz2UrmP9r4/Cdy2ne0aRs3OYhSK6GwGnVur+/fKMYsFtMeprevJz+IpFmn3Amm3V+XIKDoDj8xSEd/J45jVeax0GisWc4LWhKRyPYU8sa89gzadVHTlocdXUs3zfQObJqW9QgixbGIC6W6kZmcxn/4y2jTBsug++RRsY9rRymTxdbvOdJdul25m9ajXbjaHzuScQg0vv0g3m8N34QLNm1Lo0NSOlAdcjzM31bj0R0FfkJ/EvlshhFgmgXQT3Bmk5YSk6vVD6ukZ1OxFVKE4ciB1p8bcs1Xc1+5PZ9m5HLUnnry0/mg2h+kamasBX6mEMj207rwbolHa+w7Q+OjH0Nkcq+sHudo2JEU57LkM15eCnM7h1TbeUgG0jWcmR3CEqvijXnvocxmSlNzo8cPX1RyS+h241sbp1I2qDY27xudWruk5Kkndit1CAukYdK8fUs1eBMtCZ7f/Ds/K5lYNMlrzmEwGZTl3rlYoTPuGG53BSDAxd3pWNsfSY5f+KLBkQJEQYpeQQDoGPT2N9eRT6P4+0q2e0LgFnP7SJ1HFAigIvfQi9NLRi48+MVHBdOWPgsl7GYUQYk0TUyJwt9LT09gf/OC2DzQaVTebo3XLrU6AMp16vJjmyp2pEEKIyyN3pFtsWJ/n0Me7trWro0gPrP7i7mBbf3UYpRU6m8W0LIxCHmVZznbvGqNOy3AbNs3jShr1UsP68ob3oW702BGniIzZR7pRv+dGq61s5lyDx8sKK0K4SSC9xljZHAuPPblmEQchhBCjk0B6DdrMACUhhBCbc+0EUnUpzbSNdfrXmL7iriSjR9pvus/oSuUq7U4F9z121BTjiNM4hp3PbZwO+mEpy4Frjfjch55vw3ONlk4dePyox4+QSpbUrRBbTwYbCSGEEGO4du5Ir1FmIY9ZLGBlspLOFUKIK0AC6Rrc6a1h65P2p9Jsd/LM9Vh32m3g1O4cgb36AdaQVG9/KtjM5wk9+zTa9KCsLrXHnsTK5fqOdV16xIo7bkNHl46RBhw1dbLlqd8tPNfAubc4FbzxuSR1K8RWk9TuVcwoFdCmB2t6Gm16MEqFnW6SEEJcdSSQXsXsdBZldTFnZ1FWFzud3ekmCSHEVeeaTO2601WjjuJdr4j9WtxpOXcFwYF0qKsx7noL7qu7CzSsOt/MNM0nnlrpI1W53IZv+MiFAEYsJDBwvTHShqMXYBjx/GPkNEe+1mVfafl6sqanEDvpmgyk1xI7l8POySAjIYS4UiS1K4QQQoxBAqkQQggxBkntbsIo02EG+kRdPWCGu+i86/Hu482BPtDVx7uL1qsR+ntH7fN0G38R6CEHbHCtUY1bQP9KdiVu5WLYIP2eQmw3CaS7nJHPYxQL2Jms9IUKIcQOkEC6ixn5PL5nngbDBNui9fiT2FK9SAghtpUEUkafDrNRqnfUevjDCpQPpIZ71zLyeTw/+D5mrYZ1000Ys7N4SgX09PqBdNxU7cDx7vMPpIq3trrQKG3Zaludft2IpGaF2F0kkO5CRj6P7ytPo2o1PK/+BAAdDqMzUnBBCCG2mwTSXUgVC2CaWDfdBIB14ADdj31c+kiFEGIHSCBdwziVj0ZO1Q5JBg9UUVIKlcti2BaqMIuaCmPf+3FUbhqTjUftjlv8fNTU7VYWWx9mO1OvbpKKFeLaJoF0F9K5adpPPolRKGJnM+jc9E43SQghrlkSSHcpnZvGkgAqhBA7TgLpFuhPK7qLNYya6h04tyv16y5672aOkGYcmnodMXU7eiF5SccKIXY/KREohBBCjEECqRBCCDEGCaRCCCHEGKSPdBNGmQ4zrMD9sD5Tt4Ei9gNt2fzcnK2uNDR8uszWdURKn6YQYlJNzB2pUupLSqnzSqmf9r4eXee4h5VSx5RSx5VSX9zudgohhBD9Ju2O9H/XWv/eejuVUibwB8BngXPAy0qpp7XWb21XA4UQQoh+kxZIh7kHOK61PgmglPpz4ClgWwPplUz1uk81tJD7Fcx5bnXqVtKzQoir0cSkdnt+Qyn1mlLqT5RSiTX27wXO9m2f6/1sTUqpLyilXlFKvVIqFre6rUIIIcT2BlKl1DeVUm+s8fUU8C+B64HbgYvA7691ijV+tu79oNb6D7XWd2ut705nMlvyHIQQQoh+25ra1Vo/sJnjlFL/GnhmjV3ngP192/uAC1vQtLH0pyzHWcsUxi/k7r78OOcbd9StpHKFENeCiUntKqVm+jZ/FnhjjcNeBm5USh1SSvmAzwFPb0f7hBBCiLVM0mCjf6KUuh3npuo08N8DKKX2AH+ktX5Ua91VSv0G8A3ABP5Ea/3mTjVYCCGEmJhAqrX+u+v8/ALwaN/2s8Cz29WuUY26lumo6VN3Knjg+lt4rWEkdSuEEBOU2hVCCCF2IwmkQgghxBgkkAohhBBjmJg+0qvVsH7EEWrOA9u7GLb0gQohxHByRyqEEEKMQQKpEEIIMQZJ7e6wUdOno6aCx7mWEEKI4eSOVAghhBiDBFIhhBBiDJLa3WUkPSuEEJNF7kiFEEKIMUggFUIIIcYggVQIIYQYgwRSIYQQYgwSSIUQQogxSCAVQgghxiCBVAghhBiDBFIhhBBiDBJIhRBCiDFIIBVCCCHGIIFUCCGEGIMEUiGEEGIMEkiFEEKIMUggFUIIIcYggVQIIYQYgwRSIYQQYgwSSIUQQogxSCAVQgghxiCBVAghhBiDBFIhhBBiDBJIhRBCiDF4droBy5RSfwEc6W3GgXmt9e1rHHcaWAQsoKu1vnvbGimEEEK4TEwg1Vr/0vL3SqnfB6obHP4prXXpyrdKCCGE2NjEBNJlSikF/JfAp3e6LUIIIcQwk9hHeh+Q11q/t85+DTynlPpbpdQXtrFdQgghxIBtvSNVSn0TmF5j129prb/c+/6/Av79Bqf5uNb6glIqCzyvlHpHa/3COtf7ArAcbFuhYPCNy237BEgDuz2dLc9hMshzmAy7/Tns9vbDpXE5Y1Fa6604z5ZQSnmA88BdWutzmzj+S8CS1vr3NnHsK7t5YNJubz/Ic5gU8hwmw25/Dru9/bB1z2HSUrsPAO+sF0SVUmGlVGT5e+BBYDffZQohhNjlJi2Qfg5XWlcptUcp9WxvMwf8jVLqVeAl4Kta669vcxuFEEKIFRM1aldr/d+u8bMLwKO9708Ct13m6f/w8ls2EXZ7+0Gew6SQ5zAZdvtz2O3thy16DhPVRyqEEELsNpOW2hVCCCF2lasmkCqlflEp9aZSylZK3e3a95tKqeNKqWNKqYfWefwhpdSPlFLvKaX+Qinl256Wr63Xhp/2vk4rpX66znGnlVKv9457ZbvbuRGl1JeUUuf7nsej6xz3cO+9Oa6U+uJ2t3MjSql/qpR6Ryn1mlLqr5RS8XWOm7j3YdjrqpTy9z5nx3uf/YPb38q1KaX2K6W+rZR6u/fv+h+sccz9Sqlq3+frt3eirRsZ9rlQjv+j9x68ppS6cyfauR6l1JG+1/enSqkFpdQ/dB0zce+DUupPlFIFpdQbfT9LKqWe7/2Of14plVjnsZ/vHfOeUurzm7qg1vqq+AI+gDMn6DvA3X0/Pwq8CviBQ8AJwFzj8f8B+Fzv+38F/PpOP6e+tv0+8Nvr7DsNpHe6jeu07UvA/zzkGLP3nhwGfL336uhOt72vfQ8Cnt73vwv87m54HzbzugJ/D/hXve8/B/zFTre7r20zwJ297yPAu2u0/37gmZ1u65DnseHnAmf8x9cABXwU+NFOt3nIZ2oWuG7S3wfgE8CdwBt9P/snwBd7339xrX/LQBI42ft/ovd9Ytj1rpo7Uq3121rrY2vsegr4c611S2t9CjgO3NN/QK8s4aeB/9T70b8F/osr2d7N6iuZuFGRit3sHuC41vqk1roN/DnOezYRtNbPaa27vc0XgX072Z4RbOZ1fQrnsw7OZ/8zvc/bjtNaX9Ra/7j3/SLwNrB3Z1t1RTwF/Kl2vAjElVIzO92odXwGOKG1fn+nGzKMdor0VFw/7v+8r/c7/iHgea11RWs9BzwPPDzseldNIN3AXuBs3/Y5Bv9BpnBWm+lucMxO2e0lE3+jl7L6k3VSKZt5fybFr+DcPaxl0t6HzbyuK8f0PvtVnH8LE6WXcr4D+NEau39GKfWqUuprSqlbtrVhmzPsc7GbPv8D0xP7TPr7AJDTWl8E5w81ILvGMZf1fkzU9Jdh1OZKDA48bI2fuYcqb+aYLbfJ57NlJROvhI2eA/AvgX+M81r+Y5wU9a+4T7HGY7d1KPlm3gel1G8BXeDfrXOaHX0f1jCxn/tRKKWmgL8E/qHWesG1+8c4acalXv/7/wfcuN1tHGLY52Li3wOA3piRJ4HfXGP3bngfNuuy3o9dFUi11g9cxsPOAfv7tvcBF1zHlHBSKp7eX+ZrHbPlhj0f5ZRM/Dngrg3OcaH3/4JS6q9wUnrb9gt8s++JUupfA8+ssWsz788VtYn34fPA48BndK8jZY1z7Oj7sIbNvK7Lx5zrfdZiDKbDdoxSyosTRP+d1vo/u/f3B1at9bNKqf9LKZXWE7TE4iY+Fzv++d+kR4Afa63z7h274X3oySulZrTWF3vp88Iax5zD6fNdtg9n3M2GroXU7tPA53ojFA/h/KX0Uv8BvV+O3wZ+ofejzwPr3eFup11dMtHV1/OzrN22l4EblTNq2oeTPnp6O9q3GUqph4F/BDypta6vc8wkvg+beV2fxvmsg/PZ/9Z6fyhst15f7R8Db2ut/9k6x0wv9+kqpe7B+X1W3r5WbmyTn4ungf+mN3r3o0B1Of04YdbNjE36+9Cn//O+3u/4bwAPKqUSva6oB3s/29hOj67aqi+cX9TngBaQB77Rt++3cEYwHgMe6fv5s8Ce3veHcQLsceA/Av4JeE7/Bvg118/2AM/2tfnV3tebOKnIHX8v+tr6Z8DrwGu9D/GM+zn0th/FGZV5YgKfw3GcPpOf9r6WR7lO/Puw1usK/A7OHwUAgd5n/Xjvs394p9vc1/Z7cVJqr/W99o8Cv7b8bwL4jd7r/SrOQLCP7XS7Xc9hzc+F6zko4A9679Hr9M04mJQvIIQTGGN9P5vo9wEn6F8EOr248Ks4/f9/DbzX+3+yd+zdwB/1PfZXev8mjgO/vJnrSWUjIYQQYgzXQmpXCCGEuGIkkAohhBBjkEAqhBBCjEECqRBCCDEGCaRCCCHEGCSQCnGN6a1u8ZdKqfeVUlop9W92uk1C7GYSSIW49vwd4HqcgtzusntCiBHtqhKBQogt8ZDW2oaVyk1CiDHIHakQV4leSbp3lFIv9erULv/8QeUseP8/ACwHUSHE1pBAKsRVQmtdw6mJehvOajv0Vh35U5yFl/9gB5snxFVLAqkQVxGt9U+ALwL/i1LqAZwgajG4fJ0QYotIH6kQV59/DnwWZ9k6H/BZPXlLWglx1ZA7UiGuMtpZieLPAD/wqtb6r3e4SUJc1SSQCnGVUUpN49yV/hi4TSn1D3a4SUJc1SSQCnEV6S2w/G+BNk56958Dv6uU+tCONkyIq5j0kQpxdfkfgQeAT2utK0qpLwL3A/9eKXW31rqhlDoKHO0dHwSuU0r9Qm/7u1rr4ra3WohdTBb2FuIqoZS6A3gR+Kda6/+17+dHcNK8f6q1/nWl1JeA/22d03xKa/2dK91WIa4mEkiFEEKIMUgfqRBCCDEGCaRCCCHEGCSQCiGEEGOQQCqEEEKMQQKpEEIIMQYJpEIIIcQYJJAKIYQQY5BAKoQQQoxBAqkQQggxhv8fjT38TgbKbtEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a set (x, y) pairs sampled along an evenly spaced grid\n",
    "stepsize = 0.2\n",
    "xmin, xmax = -10, 10\n",
    "ymin, ymax = -7.5, 12.5\n",
    "xx, yy = np.meshgrid(np.arange(xmin,xmax,stepsize), np.arange(ymin,ymax,stepsize))\n",
    "xy = np.array([xx.ravel(), yy.ravel()]).T\n",
    "\n",
    "# Evaluate the density at the above (x,y) pairs.\n",
    "z = np.exp(kde.score_samples(xy))\n",
    "z_min, z_max = -np.abs(z).max(), np.abs(z).max()\n",
    "zz = z.reshape(xx.shape) # Reshape the result so we can use it with \"pcolormesh\" below.\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(7,6))\n",
    "plt.pcolormesh(xx, yy, zz, cmap='RdBu', vmin=z_min, vmax=z_max)\n",
    "plt.scatter(X[:,0], X[:,1], alpha=0.3, s=10, c='red')\n",
    "plt.xlim(xmin, xmax)\n",
    "plt.ylim(ymin, ymax)\n",
    "plt.xlabel(\"x1\", fontsize=16)\n",
    "plt.ylabel(\"x2\", fontsize=16)\n",
    "plt.title(\"KDE in 2D\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The previous density estimate was done with a bandwidth of 1. Let's change the bandwidth to 2 and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'KDE in 2D')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kde = KernelDensity(kernel='gaussian', bandwidth=2)\n",
    "kde.fit(X)\n",
    "\n",
    "stepsize = 0.2\n",
    "xmin, xmax = -10, 10\n",
    "ymin, ymax = -7.5, 12.5\n",
    "xx, yy = np.meshgrid(np.arange(xmin,xmax,stepsize), np.arange(ymin,ymax,stepsize))\n",
    "xy = np.array([xx.ravel(), yy.ravel()]).T\n",
    "\n",
    "z = np.exp(kde.score_samples(xy))\n",
    "z_min, z_max = -np.abs(z).max(), np.abs(z).max()\n",
    "zz = z.reshape(xx.shape)\n",
    "\n",
    "plt.figure(figsize=(7,6))\n",
    "plt.pcolormesh(xx, yy, zz, cmap='RdBu', vmin=z_min, vmax=z_max)\n",
    "plt.scatter(X[:,0], X[:,1], alpha=0.3, s=10, c='red')\n",
    "plt.xlim(xmin, xmax)\n",
    "plt.ylim(ymin, ymax)\n",
    "plt.xlabel(\"x1\", fontsize=16)\n",
    "plt.ylabel(\"x2\", fontsize=16)\n",
    "plt.title(\"KDE in 2D\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2: \n",
    "Change the bandwidth parameter above to different values (0.1, 0.5, 2.5, 3.0, etc) and plot the resulting density. Make sure you understand the results. Essentially, as the bandwidth increases, each data point, exerts its influence over a larger region of the feature space.\n",
    "\n",
    "### Exercise 3:\n",
    "Use grid search to determine the best bandwidth and plot the corresponding estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KDE as a Generative Model\n",
    "\n",
    "Given a density estimate, we can use it to generate new samples that reflect the underlying data distribution (assuming that the estimate is a good representation of the distribution). For example, given a dataset containing a customer's past transactions, we can fit a KDE and use that KDE to generate new transactions that follow the same pattern as the original. If the real data is bimodal, the artificially generated data will also be bimodal. In fact, you can generate as many new datasets as you want and use those in creative ways. For example, if the original data corresponds to fradulant behavior (or, in the cyber-security domain, a network invasion), we can use the synthetic datasets as additional data for training or testing our models.\n",
    "\n",
    "Let us illustrate the process of generating new samples using the amounts2 data that we saw earlier. The data is printed below for convenience.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([19.89, 22.34, 28.61, 23.03, 20.24, 18.43, 24.69, 26.54, 21.71,\n",
       "       19.37, 22.08, 14.7 , 17.78, 25.24, 23.77, 18.87, 24.74, 16.86,\n",
       "       23.33, 26.66, 23.15, 18.16, 19.79, 11.85, 19.06, 18.84, 22.89,\n",
       "        9.07, 13.67, 17.36, 22.5 , 25.44, 12.68, 17.29, 25.79, 25.1 ,\n",
       "       19.82, 16.18, 27.22, 21.67, 19.41, 22.18, 15.82, 16.07, 14.97,\n",
       "       19.39, 16.76, 19.5 , 29.54, 23.48, 43.18, 51.7 , 47.72, 45.43,\n",
       "       51.93, 42.88, 48.86, 47.01, 47.28, 49.33, 46.59, 46.55, 53.62,\n",
       "       49.17, 51.52, 48.69, 53.51, 50.52, 45.78, 47.66, 44.11, 49.69,\n",
       "       50.2 , 52.9 , 51.2 , 51.42, 50.48, 52.47, 53.27, 53.68, 49.41,\n",
       "       52.13, 51.16, 54.65, 50.29, 50.97, 55.9 , 45.01, 49.62, 57.09,\n",
       "       55.51, 50.23, 51.13, 44.93, 51.87, 56.45, 53.77, 50.85, 50.49,\n",
       "       52.51])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "amounts2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first fit a KDE with a bandwidth of 5 and plot the density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20f2317c608>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Instantiate\n",
    "kde = KernelDensity(kernel='gaussian', bandwidth=5)\n",
    "# Fit. We need to reshape the 1-D array x into 2-D first\n",
    "kde.fit(x.reshape(-1, 1))\n",
    "\n",
    "# Our data values lie in the range [9.07, 57.09]. i.e., x.min() = 9.07 and x.max() = 57.09\n",
    "# Let create a plot that covers the range [0, 65]\n",
    "# Generate 100 evenly spaced points in the range [0, 65]\n",
    "xx = np.linspace(0, 65, 100)\n",
    "\n",
    "# Let us compute the densities at those 100 points. Note the use of np.exp to convert log-densities to densities\n",
    "yy = np.exp(kde.score_samples(xx.reshape(-1,1)))\n",
    "\n",
    "# Plot\n",
    "plt.plot(xx, yy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen from the above plot, the density is bimodal with peaks near 20 and 50, and it is practically zero for values outside the range \\[0, 60\\]. Thus, if we sample from this distribution, there will be a lot of samples closer to 20 or 50, and very few samples below 0 or above 60. \n",
    "\n",
    "To sample from this distribution, we use the \"sample\" method and specify the number of samples we want. The code in the next cell, samples 5 data points from the above density. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[47.71637973],\n",
       "       [59.53962224],\n",
       "       [52.92059265],\n",
       "       [49.4006173 ],\n",
       "       [28.54600389]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kde.sample(n_samples=5, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's generate 300 samples and print the first 100 values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[52.71253269 50.85090518 43.60341966 50.74039135  8.69969546 49.05340058\n",
      "  13.35569262 59.17025023 47.98908784 31.12599051 61.15242272 37.37007487\n",
      "  50.99129365 54.51454018 23.35281487 19.72364093 27.94559711 53.1610456\n",
      "  50.92493515 36.62998097 56.61165782 59.07809296 12.6931787  45.93787836\n",
      "  17.30532438 46.29106015 24.47976582 50.27335791 51.17769376 25.65374572\n",
      "  19.26201311 45.55318022 11.47530801 51.9118969  16.39570371 44.01591823\n",
      "  43.56842981 46.28716352 42.18860097 46.72389298 27.71945512 16.51211044\n",
      "  46.10556914 25.17700083 55.50523173 36.65703622 27.93956154 19.73046661\n",
      "  22.17795709 17.86523312 49.47870889 15.4894803  40.33657766 32.40246431\n",
      "  22.59729671 29.84086356 45.22975076 26.52188527 18.19171844 22.10421917\n",
      "  13.64373317 20.75572645 52.13909082 31.74923115 23.5195622  17.41486441\n",
      "  62.67958349 14.06992089 53.9702515  25.05445681 51.33862484 19.6747684\n",
      "  48.85275485 48.44027944 46.36736574 31.3206534  13.07917977 14.37910898\n",
      "  20.69191541 12.39640106 18.76870764 15.44641247 28.15886576 46.86213281\n",
      "  48.1914922  28.27871903 42.08587096 15.71661124 45.08560095 51.60175795\n",
      "  25.22914274 52.07556404 24.93186799 49.15347362 10.07197806 19.26503506\n",
      "  48.65258179 24.15542459 45.3732237  18.32853874]]\n"
     ]
    }
   ],
   "source": [
    "samples = kde.sample(n_samples=300, random_state=0)\n",
    "print(samples[:100].T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have just created a \"fake\" customer transactions dataset that has a similar distribution as the original \"accounts2\" data. Here is the histogram of the sampled data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([0.00678848, 0.0158398 , 0.02319399, 0.01923404, 0.01470838,\n",
       "        0.0079199 , 0.01470838, 0.03111389, 0.02489111, 0.01131414]),\n",
       " array([ 4.08190454,  9.97423586, 15.86656719, 21.75889852, 27.65122984,\n",
       "        33.54356117, 39.4358925 , 45.32822383, 51.22055515, 57.11288648,\n",
       "        63.00521781]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(samples, normed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating synthetic hand-written digits\n",
    "\n",
    "The scikit-learn documentation has an interesting example on using KDE as a generative model. The example uses a data set of hand-written digits where each digit is a square image of size 8x8, which, when flattened, yields an array of size 64. PCA is then used to reduce the dimensionality of the data from 64 to 15, and a KDE is fit to the resulting 15-dimensional data. Having fit a KDE, new samples are drawn from the distribution where each new sample is 15-dimensional. The 15-dimensional synthetic samples are then conveted back to the original 64-dimensional space and displayed. The resulting images look very much like hand-written digits. See [here](http://scikit-learn.org/stable/auto_examples/neighbors/plot_digits_kde_sampling.html#sphx-glr-auto-examples-neighbors-plot-digits-kde-sampling-py) for the complete example.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Speeding up computations\n",
    "\n",
    "Kernel density estimation is computationally very expensive. This is not surprising given that the process involves placing a Gaussian at each observation and summing up their contributions. If there are 100,000 observations, then to compute the density at any given point, we have to essentially evaluate 100,000 Gaussians at that point and sum up the values. However, if we are willing to cut corners, then when evaluating the density at a given point, we can safely ignore Gaussians that are centered far away from that point because their values will be close to zero. Scikit-learn uses a tree-based data structure to speed up computations, and it also allows you to specify a tolerance level for the estimates - a larger tolerance will lead to faster execution but lower accuracy. There are two parameters to specify tolerance: \"atol\" and \"rtol\". The first specifies an absolute tolerance (default = 0), and the second specifies a relative tolerance (default = 1E-8). For more information, please refer to https://jakevdp.github.io/blog/2013/12/01/kernel-density-estimation/. This blog post has a plot of computational time vs. relative tolerance. It also has brief discussion of the underlying data structure and the approximation used."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions\n",
    "\n",
    "Kernel density estimation is a popular approach for estimating the underlying probability density of the data. It is a non-parameteric approach in that it does not assume a parametric model for the density and it learns the shape of the underlying density automatically (subject to the bandwidth and kernel parameters we discussed above). KDE is a very useful tool in data analysis, and In the next chapter, we will look at a Capital One use case involving credit card fraud."
   ]
  }
 ],
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