Kernel Adaptive Sequential Monte Carlo

Heiko Stratmann, Dino Sejdinovic, Brooks Paige and myself had a poster on our work on Kernel Adaptive SMC (arXiv) at the Scalable Inference NIPS workshop this year. The basic idea is very related to Dinos paper on Kernel-informed MCMC, in that the particle system is (implicitly) mapped to a function space (the infamous Reproducing Kernel Hilbert Space) and used to inform a sample from a Gaussian fit to the functional associated with samples. As always, things that are nasty and nonlinear in the input space behave much more nicely in feature space. An when your name is Dino Sejdinovic, you can actually integrate out all steps in feature space, ending up with a Gaussian proposal in the space you actually want to sample from.

In the title cartoon, our approach (in red, called KASS for Kernel Adaptive SMC sampler) lines up nicely with the support of the target distribution. ASMC by Fearnhead et al., or at least the sampler they use in their evaluation, which is a special case of our method, cannot adapt to this nonlinear structure. This results in better performance for KASS compared to ASMC and Random Walk SMC, as measured by Maximum Mean Discrepancy.Capture d’écran 2015-12-18 à 17.31.43.pngHowever, this of course comes at the price of higher computational complexity, similar to related methods such as Riemannian Manifold MALA/HMC. If your dataset is large however and evaluating the likelihood majorizes evaluating the Gram matrix on your particle system, this method will still have an edge over others when the support is nonlinear. For the MCMC predecessor KAMH/Kameleon see Heikos post.

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