Kernel Sequential Monte Carlo
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by
Ingmar Schuster, Heiko Strathmann, Brooks Paige, Dino Sejdinovic
2017
Abstract
We propose kernel sequential Monte Carlo (KSMC), a framework for sampling
from static target densities. KSMC is a family of sequential Monte Carlo
algorithms that are based on building emulator models of the current particle
system in a reproducing kernel Hilbert space. We here focus on modelling
nonlinear covariance structure and gradients of the target. The emulator's
geometry is adaptively updated and subsequently used to inform local proposals.
Unlike in adaptive Markov chain Monte Carlo, continuous adaptation does not
compromise convergence of the sampler. KSMC combines the strengths of sequental
Monte Carlo and kernel methods: superior performance for multimodal targets and
the ability to estimate model evidence as compared to Markov chain Monte Carlo,
and the emulator's ability to represent targets that exhibit high degrees of
nonlinearity. As KSMC does not require access to target gradients, it is
particularly applicable on targets whose gradients are unknown or prohibitively
expensive. We describe necessary tuning details and demonstrate the benefits of
the the proposed methodology on a series of challenging synthetic and
real-world examples.
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