Add ApproximatePeriodicKernel

[theogf]

This is an attempt at #61

Left todo:

• Add tests for the ApproxPeriodicKernel

[theogf]

Will be splitted to treat the KernelSum first.

[theogf]

Work in progress:

• The basic functionality is implemented with the CosineKernel
• However the logpdf prediction seems to fail, which indicates there might be an error somewhere in the conversion of the kernel to state-space, needs to investigate

[theogf]

This will need some fixes from #100 but ready otherwise

[theogf]

Another issue is with the argument for the PeriodicKernel, it is bounded but we do not do any transformation. This is messing up computations when using FiniteDifferences

[simsurace]

Looks clean. Maybe a few tests comparing a normal GP to a temporal GP with ApproxPeriodixKernel would add some safety, e.g. comparing the logpdf output and maybe posterior mean and variance.

[theogf]

Looks clean. Maybe a few tests comparing a normal GP to a temporal GP with ApproxPeriodixKernel would add some safety, e.g. comparing the logpdf output and maybe posterior mean and variance.

This is already the case! If you look at the lti_sde tests, the prior is compared against a "naive" GP.

[simsurace]

This is already the case! If you look at the lti_sde tests, the prior is compared against a "naive" GP.

Indeed, thanks!

[coveralls]

Pull Request Test Coverage Report for Build 4817610971

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• 55 of 59 (93.22%) changed or added relevant lines in 3 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.3%) to 87.977%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
src/models/lgssm.jl	0	1	0.0%
src/gp/lti_sde.jl	54	57	94.74%

Totals
Change from base Build 4817383865:	0.3%
Covered Lines:	1361
Relevant Lines:	1547

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💛 - Coveralls

[theogf]

@willtebbutt this is fully ready for a review.

[simsurace]

@willtebbutt are there any blockers for this?

[willtebbutt]

Nope, no blockers really. I'm happy for this to be merged