# Kernel Sequential Monte Carlo

## 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.

## Notes

### Acknowledgments

I.S. was supported by a PSL postdoc grant and DFG through grant CRC 1114 “Scaling Cascades in Complex Systems”, Project B03 “Multilevel coarse graining of multiscale problems”. H.S. was supported by the Gatsby Chaitable foundation. B.P. was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1.

## Supplementary material

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