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