Kernel Sequential Monte Carlo

TL;DR

Kernel Sequential Monte Carlo (KSMC) introduces a novel framework combining kernel methods with sequential Monte Carlo to efficiently sample complex, multimodal, and nonlinear target distributions without requiring gradient information.

Contribution

KSMC is a new family of algorithms that models nonlinear covariance and gradients using kernel emulators, enhancing sampling performance and applicability to gradient-inaccessible targets.

Findings

KSMC outperforms traditional methods on synthetic examples.

It effectively handles multimodal and nonlinear targets.

Demonstrates superior model evidence estimation.

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.