Kernel Adaptive Sequential Monte Carlo

We develop and study the Kernel Adaptive SMC (Sequential Monte Carlo) Sampler - KASS. KASS builds on the adaptive Sequential Monte Carlo (ASMC) sampler by Fearnhead (2013) marrying it with the kernel-based MCMC rejuvenation step based on Sejdinovic et al. (2014) - resulting in a novel methodology for efficient sampling from multimodal and multivariate target distributions with nonlinear dependencies. The key step involves representing the current re-weighted SMC particle system in a reproducing kernel Hilbert space - covariance therein informs Metropolis-Hastings moves for rejuvenating particles. This allows harvesting advantages of the two approaches: on one side, the superior performance of SMC on multi-modal targets as well as its ability to estimate model evidence; on the other, the rejuvenation moves that locally adapt to a non-linear covariance structure of the target. Moreover, KASS does not require computing gradients of the target distribution and is thus suitable for IS/SMC algorithms for intractable likelihoods, where analytic gradients are not available. Our focus is on static target distributions: KASS defines a sequence from a simple distribution (such as the prior in a Bayesian inference setting) to the target of interest (e.g. a Bayesian posterior). We demonstrate strengths of the proposed methodology on a series of examples, demonstrating improved convergence on nonlinear targets, better mode recovery in a sensor localisation problem as well as a more accurate model evidence estimation in Gaussian Process Classification.