Optimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fourth-cliff",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pylab as plt"
   ]
  },
  {
   "source": [
    "# Take a look at Data"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "severe-completion",
   "metadata": {},
   "outputs": [],
   "source": [
    "RF = pd.read_csv(\"RForest_sample_submission_ml.csv\")\n",
    "RFF = pd.read_csv(\"RForest_sample_submission_ml2.csv\")\n",
    "\n",
    "LGBM = pd.read_csv(\"LGBM_sample_submission_ml.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "endless-mainstream",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>updates</th>\n",
       "      <th>personal</th>\n",
       "      <th>promotions</th>\n",
       "      <th>forums</th>\n",
       "      <th>purchases</th>\n",
       "      <th>travel</th>\n",
       "      <th>spam</th>\n",
       "      <th>social</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.991095</td>\n",
       "      <td>0.000089</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.999911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.998963</td>\n",
       "      <td>0.999923</td>\n",
       "      <td>0.000681</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.000050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.999923</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.550957</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.000050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.999950</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.999950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.999950</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.212526</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.000050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16997</th>\n",
       "      <td>16997</td>\n",
       "      <td>0.000077</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.999950</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.000050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16998</th>\n",
       "      <td>16998</td>\n",
       "      <td>0.004676</td>\n",
       "      <td>0.021388</td>\n",
       "      <td>0.993294</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.000050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16999</th>\n",
       "      <td>16999</td>\n",
       "      <td>0.013259</td>\n",
       "      <td>0.193577</td>\n",
       "      <td>0.000208</td>\n",
       "      <td>0.242133</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.000050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17000</th>\n",
       "      <td>17000</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.999950</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.000050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17001</th>\n",
       "      <td>17001</td>\n",
       "      <td>0.001393</td>\n",
       "      <td>0.984243</td>\n",
       "      <td>0.000089</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000065</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.00005</td>\n",
       "      <td>0.000089</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>17002 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Id   updates  personal  promotions    forums  purchases   travel  \\\n",
       "0          0  0.000050  0.991095    0.000089  0.000050   0.000050  0.00005   \n",
       "1          1  0.998963  0.999923    0.000681  0.000050   0.000050  0.00005   \n",
       "2          2  0.000050  0.999923    0.000050  0.550957   0.000050  0.00005   \n",
       "3          3  0.000050  0.999950    0.000050  0.000050   0.000050  0.00005   \n",
       "4          4  0.000050  0.999950    0.000050  0.212526   0.000050  0.00005   \n",
       "...      ...       ...       ...         ...       ...        ...      ...   \n",
       "16997  16997  0.000077  0.000050    0.000050  0.999950   0.000050  0.00005   \n",
       "16998  16998  0.004676  0.021388    0.993294  0.000050   0.000050  0.00005   \n",
       "16999  16999  0.013259  0.193577    0.000208  0.242133   0.000050  0.00005   \n",
       "17000  17000  0.000050  0.000050    0.000050  0.999950   0.000050  0.00005   \n",
       "17001  17001  0.001393  0.984243    0.000089  0.000050   0.000065  0.00005   \n",
       "\n",
       "          spam    social  \n",
       "0      0.00005  0.999911  \n",
       "1      0.00005  0.000050  \n",
       "2      0.00005  0.000050  \n",
       "3      0.00005  0.999950  \n",
       "4      0.00005  0.000050  \n",
       "...        ...       ...  \n",
       "16997  0.00005  0.000050  \n",
       "16998  0.00005  0.000050  \n",
       "16999  0.00005  0.000050  \n",
       "17000  0.00005  0.000050  \n",
       "17001  0.00005  0.000089  \n",
       "\n",
       "[17002 rows x 9 columns]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "defensive-spare",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5Dcb8OeC/ga8Ov/bMuuZpj3nFvjcx57NlRnyfw6AddTdwB3DJrGtegzFvAr7AYCbNV4HfmHXNY453N/B14FEGf4ltA3YAO5a9x1cNvx93TOLn2tsPSFJD89KWkSStguEuSQ0Z7pLUkOEuSQ0Z7pLUkOEuSQ0Z7pLU0P8BSiO0lTa3qS8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7RatcWZuBX+9mzZwKzFXVV4ZqcdJnkZdxtvlMekcsXwau7Ja9i94PN/Te/I8D24F/BU6YdM0r0OdPA08A93Rfmydd87j7PG/b25jy2TIDvs+hNxz1APBF4IJJ17wCfV4DfI7eTJp7gF+cdM1D9ncT8BXgOXp/iV0MXApc2vceX9P9f3xxFN/XXn5Akho0LcMykqRlMNwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSg/4P1fCiXkReRAsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EPG5y+N3vAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VfXegI076KvIZXG2+hs4ZywvA57tjX6Dzww2dF/8B4BDwb8Blk655DHP+Z+B7wNPdP7snXfOo5zxj38dY4Ktl+nydQ6cd9RzwLWDTpGsew5zXAo/TWUnzNPCbk655wPneB3wXeJ3Ob2JbgFuAW3pe4+3dv49vDePftR8/IEkNWihtGUnSGTDcJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoP+DzKWHGlvJx5+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/5Y5Fl5/tTzM4aifJWgZtmkNTrHHcusz534BLAJJcxCDcj0+1yunaB/z6cNXMm4ETVfXVkUbs+yzyMs42v53BEcsTwIeG2z7K4B83DN78vwLmgC8Ar+675inM+e+B/wAeHP7Z13fNk57zgn3vZZWvlun4PodBO+pR4CvAFX3XPIU5bwY+x2AlzYPAz/dd84jzvRX4KvBtBr+J7QSuAq6a9x7fOPz7+Mo4fq69/IAkNWi1tGUkSctguEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QG/T/k4/cBxEjwOQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = ['updates', 'personal', 'promotions','forums', 'purchases', 'travel','spam', 'social']\n",
    "for lab in labels :    \n",
    "    plt.hist(RF[lab], bins=15)\n",
    "    plt.title(lab)\n",
    "    plt.yscale('log')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "roman-rental",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cJamh/wcRO0B2eJy/fgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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y+qr67iSLGrMtwO6q+kSSnwX+NsmVVfXcpAtbKpbKnnuX+7X+eJ0kK+j9KPftRaluPDrdozbJ24GPAtdV1Q8WqbZxmW/OLwOuBO5Jcpxeb3LfEj+o2uVzPgnsq6pnquprwL/TC/ulqsuctwJ7AarqEPASehfYatXQ96SebamEe5f7te4D3td//C7gX6p/pGKJmnfOSd4A/AW9YF/qfViYZ85VdaaqVlbVVFVN0TvOcF1VHZ5MuSPR5bv9OXp77SRZSa9Nc2wRaxy1LnP+T+BtAEleRy/cTy9qlYtrH/De/lkzbwHOVNU3h9ripI8iL+Bo8zvo7bE8Dny0P/Yxev+4offhfxY4Cvwr8JpJ17wIc/4n4FvAg/0/+yZd87jnPGvde1jiZ8t0/JxDrx31CPBVYPOka16EOU8D99I7k+ZB4NcnXfOQ870d+CbwDL2fxLYCNwE3DXzGO/t/H18dxffayw9IUoOWSltGkrQAhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lq0P8B8EKFUmVIxngAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2TrrmMYx5DfAFelfSPAT87KRrHnC8u4GvAt+i95vYZmArsHXOZ3xr/8/jkWH8XLv8gCQ1aFraMpKk02C4S1KDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAb9H6Rl4RzDFuPsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = ['updates', 'personal', 'promotions','forums', 'purchases', 'travel','spam', 'social']\n",
    "for lab in labels :    \n",
    "    plt.hist(RFF[lab], bins=15)\n",
    "    plt.title(lab)\n",
    "    plt.yscale('log')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "interstate-juvenile",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAOvUlEQVR4nO3df6zddX3H8edLOmpELM7WbELx4kRi435o7pBly2TTbYUKNZtxdDjn0tEVh8ky/7AGsjCmCfyxxRBJtIsMt4Vi5x+mDTUYNwmJA0YRx8+wFFbWAluLwJ1TEZD3/jhfkrPLbXva86v3c5+P5Cbn++N8z/tzz72vfu/7+znfpqqQJLXlVdMuQJI0eoa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdpSpLMJKkky6Zdi9pjuEtSgwx3LXmeOatFhrsWtSR7k3wqyYNJnknyt0le3W17f5LvJHk2yb8k+bl5z/tkknuB7ydZ1i0/nuR7SR5O8t5u3+VJPpvkie7rs0mWd9vOTbI/ySeSHEjyZJI/7HuddUnuSfI/SfYluXKy3yEtVYa7WnAx8FvAzwBvA65I8k7geuCPgTcAXwB2vBzKnQ3AOuCU7rmXAb9YVSd3x9vb7Xc5cA7wC8DPA2cDV/Qd56eAFcCpwEbguiSv77Z9H/hI9xrrgEuTfGAUg5YOx3BXCz5XVfuq6mngM/RCexPwhaq6s6p+XFVfAn5EL6Rfdm33vB8CPwaWA2uS/ERV7a2qR7r9LgauqqoDVXUQ+Avg9/uO80K3/YWq2gX8L3AWQFXdWlX3VdVLVXUvsA14z7i+EdLLDHe1YF/f48eANwFvBj7RtWSeTfIssLrb9ornVdUe4E+BK4EDSW5K8vK+b+qOO/81Xvbdqnqxb/kHwGsBkrw7yTeTHEwyB2wGVh7rQKVBGe5qweq+x6cDT9AL7s9U1Sl9X6+pqm19+/6/W6JW1Y1V9Sv0/mEo4Jpu0xPduvmvMYgbgR3A6qpaAXweyIDPlY6Z4a4W/EmS05L8JL3++JeBvwE2d2fOSXJSd3Hz5IUOkOSsJL/e9eSfA34IvNRt3kavj78qyUrgz4F/GLC2k4Gnq+q5JGcDv3fsw5QGZ7irBTcCXwceBR4BPl1Vu4FLgM8BzwB7gI8e5hjLgauBp4D/At4IfKrb9mlgN3AvcB/w7W7dID4GXJXke/T+Udg+6KCkYcT/rEOLWZK9wB9V1TemXYt0PPHMXZIaZLhLUoNsy0hSgzxzl6QGHRc3TFq5cmXNzMxMuwxJWlTuvvvup6pq1ULbjotwn5mZYffu3dMuQ5IWlSSPHWqbbRlJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSg46LDzFJ0mIws+XmkR9z79XrRn5M8MxdkppkuEtSgwx3SWqQ4S5JDTLcJalBYwn3JCcl2Z3k/eM4viTp8AYK9yTXJzmQ5P5569cmeTjJniRb+jZ9Etg+ykIlSYMb9Mz9BmBt/4okJwDXAecBa4ANSdYk+Q3gQeDACOuUJB2FgT7EVFW3JZmZt/psYE9VPQqQ5CZgPfBa4CR6gf/DJLuq6qX5x0yyCdgEcPrppx/zACRJrzTMJ1RPBfb1Le8H3l1VlwEk+Sjw1ELBDlBVW4GtALOzszVEHZKkecZ2+4GqumFcx5YkHd4ws2UeB1b3LZ/WrZMkTdkw4X4XcGaSM5KcCFwE7DiaAyS5IMnWubm5IcqQJM036FTIbcDtwFlJ9ifZWFUvApcBtwAPAdur6oGjefGq2llVm1asWHG0dUuSDmPQ2TIbDrF+F7BrpBVJkoY21dsP2JaRpPGYarjblpGk8fDGYZLUIMNdkhpkz12SGmTPXZIaZFtGkhpkuEtSg+y5S1KD7LlLUoNsy0hSgwx3SWqQ4S5JDTLcJalBzpaRpAY5W0aSGmRbRpIaZLhLUoMMd0lqkOEuSQ1ytowkNcjZMpLUINsyktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGuyQ1yA8xSVKDlk3zxatqJ7Bzdnb2kmM9xsyWm0dYUc/eq9eN/JiSNEm2ZSSpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGuyQ1yHvLSFKD/A+yJalBtmUkqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lq0MjDPcnbk3w+yVeSXDrq40uSjmygcE9yfZIDSe6ft35tkoeT7EmyBaCqHqqqzcCHgF8efcmSpCMZ9Mz9BmBt/4okJwDXAecBa4ANSdZ02y4EbgZ2jaxSSdLABgr3qroNeHre6rOBPVX1aFU9D9wErO/231FV5wEXH+qYSTYl2Z1k98GDB4+teknSgpYN8dxTgX19y/uBdyc5F/htYDmHOXOvqq3AVoDZ2dkaog5J0jzDhPuCqupW4NZRH1eSNLhhZss8DqzuWz6tWzewJBck2To3NzdEGZKk+YYJ97uAM5OckeRE4CJgx9EcoKp2VtWmFStWDFGGJGm+QadCbgNuB85Ksj/Jxqp6EbgMuAV4CNheVQ+Mr1RJ0qAG6rlX1YZDrN/FENMdk1wAXPDWt771WA8hSVrAVG8/YFtGksbDe8tIUoMMd0lq0FTD3amQkjQe9twlqUG2ZSSpQYa7JDXIcJekBnlBVZIa5AVVSWqQbRlJapDhLkkNMtwlqUFeUJWkBnlBVZIaZFtGkhpkuEtSgwx3SWqQ4S5JDTLcJalBToWUpAY5FVKSGmRbRpIaZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIee6S1CDnuUtSg2zLSFKDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ95aRpAZ5bxlJapBtGUlqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhq0bBwHTfIBYB3wOuCLVfX1cbyOJGlhA5+5J7k+yYEk989bvzbJw0n2JNkCUFVfrapLgM3A7462ZEnSkRxNW+YGYG3/iiQnANcB5wFrgA1J1vTtckW3XZI0QQOHe1XdBjw9b/XZwJ6qerSqngduAtan5xrga1X17YWOl2RTkt1Jdh88ePBY65ckLWDYC6qnAvv6lvd36z4OvA/4YJLNCz2xqrZW1WxVza5atWrIMiRJ/cZyQbWqrgWuHcexJUlHNuyZ++PA6r7l07p1A0lyQZKtc3NzQ5YhSeo3bLjfBZyZ5IwkJwIXATsGfXJV7ayqTStWrBiyDElSv6OZCrkNuB04K8n+JBur6kXgMuAW4CFge1U9MJ5SJUmDGrjnXlUbDrF+F7BrZBVJkoY21dsP2HOXpPGYarjbc5ek8fDGYZLUIMNdkhpkz12SGjSWT6gOqqp2AjtnZ2cvmWYd881suXmkx9t79bqRHk+SjsS2jCQ1yHCXpAbZc5ekBjnPXZIaNNULqpI0TqOeHLGY2HOXpAYZ7pLUIMNdkhrkbBlJapCzZSSpQc6WmQBvZyBp0uy5S1KDDHdJapDhLkkNcraMJDXI2TKS1CBnyyxCzr5Rq5byvWBGzZ67JDXIM3dpifAvvqXFM3dJapBn7pKOif3x45tn7pLUIMNdkhrkh5gkqUF+iEmSGuQFVY3lwtiop8k5jU86OvbcJalBnrlLxymnGmoYnrlLUoM8c9eStBiuM0jDMNw1FrYUpOmyLSNJDTLcJalBhrskNcjbD0hSg7z9gCQ1yLaMJDXIcJekBhnuktQgw12SGmS4S1KDvP2ANCLeckHHE8/cJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lqkOEuSQ0y3CWpQamqaddAkoPAY8f49JXAUyMsZzFwzEuDY14ahhnzm6tq1UIbjotwH0aS3VU1O+06JskxLw2OeWkY15hty0hSgwx3SWpQC+G+ddoFTIFjXhoc89IwljEv+p67JOmVWjhzlyTNY7hLUoMWTbgnWZvk4SR7kmxZYPvyJF/utt+ZZGYKZY7UAGP+syQPJrk3yT8lefM06hylI425b7/fSVJJFv20uUHGnORD3Xv9QJIbJ13jqA3ws316km8muaf7+T5/GnWOSpLrkxxIcv8htifJtd33494k7xr6RavquP8CTgAeAd4CnAj8G7Bm3j4fAz7fPb4I+PK0657AmH8NeE33+NKlMOZuv5OB24A7gNlp1z2B9/lM4B7g9d3yG6dd9wTGvBW4tHu8Btg77bqHHPOvAu8C7j/E9vOBrwEBzgHuHPY1F8uZ+9nAnqp6tKqeB24C1s/bZz3wpe7xV4D3JskEaxy1I465qr5ZVT/oFu8ATptwjaM2yPsM8JfANcBzkyxuTAYZ8yXAdVX1DEBVHZhwjaM2yJgLeF33eAXwxATrG7mqug14+jC7rAf+rnruAE5J8tPDvOZiCfdTgX19y/u7dQvuU1UvAnPAGyZS3XgMMuZ+G+n9y7+YHXHM3Z+rq6uqlf+NepD3+W3A25J8K8kdSdZOrLrxGGTMVwIfTrIf2AV8fDKlTc3R/r4f0bKhytFxIcmHgVngPdOuZZySvAr4a+CjUy5l0pbRa82cS++vs9uS/GxVPTvNosZsA3BDVf1Vkl8C/j7JO6rqpWkXtlgsljP3x4HVfcundesW3CfJMnp/yn13ItWNxyBjJsn7gMuBC6vqRxOqbVyONOaTgXcAtybZS683uWORX1Qd5H3eD+yoqheq6j+Af6cX9ovVIGPeCGwHqKrbgVfTu8FWqwb6fT8aiyXc7wLOTHJGkhPpXTDdMW+fHcAfdI8/CPxzdVcqFqkjjjnJO4Ev0Av2xd6HhSOMuarmqmplVc1U1Qy96wwXVtXu6ZQ7EoP8bH+V3lk7SVbSa9M8OsEaR22QMf8n8F6AJG+nF+4HJ1rlZO0APtLNmjkHmKuqJ4c64rSvIh/F1ebz6Z2xPAJc3q27it4vN/Te/H8E9gD/Crxl2jVPYMzfAP4b+E73tWPaNY97zPP2vZVFPltmwPc59NpRDwL3ARdNu+YJjHkN8C16M2m+A/zmtGsecrzbgCeBF+j9JbYR2Axs7nuPr+u+H/eN4ufa2w9IUoMWS1tGknQUDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUoP8Dat/FK6GeVaYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qmquqdVU1U1Uz9OYZLqiqPZMpdyQG+d7+KL2rdpKsozdMs28Zaxy1Qfr838DZAEleTC/cDy1rlctrJ/Cr3aqZlwNzVfXloVqc9CzyEmabz6V3xfJF4K3dtnfQ++GG3pv/YWAv8G/ACydd8zL0+RPAw8Dnuq+dk6553H2ed+wtTPlqmQHf59AbjroX+Dxw8aRrXoY+bwI+TW8lzeeAX5h0zUP2dwfwZeAJen+JXQpcDlze9x5f0/3/+Pwovq+9/YAkNWhahmUkSUtguEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QG/T/XOtoVPE16UQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "labels = ['updates', 'personal', 'promotions','forums', 'purchases', 'travel','spam', 'social']\n",
    "for lab in labels :    \n",
    "    plt.hist(LGBM[lab], bins=15)\n",
    "    plt.title(lab)\n",
    "    plt.yscale('log')\n",
    "    plt.show()"
   ]
  },
  {
   "source": [
    "# Optimization"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "herbal-success",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x19909eac7f0>]"
      ]
     },
     "execution_count": 163,
     "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": [
    "X = np.linspace(0,1,1000)\n",
    "\n",
    "XX = np.sin((X-0.5)*np.pi)/2 +0.5\n",
    "\n",
    "plt.plot(X,np.sin((XX-0.5)*np.pi)/2 +0.5)\n",
    "plt.plot(X,np.sin((X-0.5)*np.pi)/2 +0.5)\n",
    "plt.plot(X,X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "wrapped-restoration",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x19909b31880>]"
      ]
     },
     "execution_count": 164,
     "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": [
    "XX = np.sin((X-0.5)*np.pi)/2 +0.5\n",
    "XXX = np.sin((XX-0.5)*np.pi)/2 +0.5\n",
    "\n",
    "plt.plot(X,(XX*2-1)*abs(XX*2-1)**0.2/2+0.5)\n",
    "plt.plot(X,X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "alien-mambo",
   "metadata": {},
   "outputs": [],
   "source": [
    "res = pd.read_csv(\"RForest_sample_submission_ml2.csv\")\n",
    "\n",
    "for lab in labels:\n",
    "    X = res[lab]\n",
    "#     X = np.sin((X-0.5)*np.pi)/2 +0.5\n",
    "    X = (X*2-1)*abs(X*2-1)**0.2/2+0.5\n",
    "    X *= 0.99999\n",
    "    X += 0.000005\n",
    "    res[lab] = X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "worthy-freedom",
   "metadata": {},
   "outputs": [],
   "source": [
    "res.to_csv('RF2 with modifications', index=False)"
   ]
  }
 ],
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