Pathwise Sampling (Take 2) #112
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rossviljoen
commented
Feb 27, 2022
rossviljoen
commented
Feb 27, 2022
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| # Computes the optimal closed form solution for the variational posterior | ||
| # q(u) (e.g. # https://krasserm.github.io/2020/12/12/gaussian-processes-sparse/ | ||
| # equations (11) & (12)). Assumes a ZeroMean function. | ||
| function optimal_variational_posterior(fu, fx, y) | ||
| fu.f.mean isa AbstractGPs.ZeroMean || | ||
| error("The exact posterior requires a GP with ZeroMean.") | ||
| σ² = fx.Σy[1] | ||
| Kuf = cov(fu, fx) | ||
| Kuu = Symmetric(cov(fu)) | ||
| Σ = (Symmetric(cov(fu) + (1 / σ²) * Kuf * Kuf')) | ||
| m = ((1 / σ²) * Kuu * (Σ \ Kuf)) * y | ||
| S = Symmetric(Kuu * (Σ \ Kuu)) | ||
| return MvNormal(m, S) | ||
| end |
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Moved this to src/sparse_variational.jl and improved it a bit
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Docs build will fail because of #105 EDIT: I think I will just remove the example from this PR and add it in a separate one once this is merged and tagged |
Codecov Report
@@ Coverage Diff @@
## master #112 +/- ##
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- Coverage 95.78% 95.42% -0.37%
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Files 4 5 +1
Lines 285 328 +43
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+ Hits 273 313 +40
- Misses 12 15 +3
Continue to review full report at Codecov.
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Supersedes #65, Closes #7
Implements pathwise sampling of functions from sparse GP posteriors from [1]
[1] https://arxiv.org/abs/2002.09309
TODO: