thangbui
Quadrature/Monte Carlo
An alternative to the currently implemented Gaussian projection and the linearisation technique in #5 is a quadrature/Monte Carlo/particle based approach.
Need code to implement this and comparison to moment matching and #5.
Notes:
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use logsumexp
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use the reparameterisation trick/store random numbers/only change them after t iterations
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high-dimensional quadratures?
Notes:
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Simple Monte Carlo for the latent variables should work for GPLVMs, GPSSMs and deep GPs with hidden variables. This should be enough because, conditioned on a latent sample, the distro of the outputs when the latent function is marginalised out for all alpha values is tractable (as a Gaussian) or can computed using quadrature. This commit is an initial attempt for GPLVMs.
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For deep GPs (as in the ICML version), simple Monte Carlo for the inducing points is needed for alpha values other than 1.