Kernel Sequential Monte Carlo

Bayesian posterior inference with Monte Carlo methods has a fundamental role in statistics and probabilistic machine learning. Target posterior distributions arising in increasingly complex models often exhibit high degrees of nonlinearity and multimodality and pose substantial challenges to traditional samplers. We propose the Kernel Sequential Monte Carlo (KSMC) framework for building emulator models of the current particle system in a Reproducing Kernel Hilbert Space and use the emulator's geometry to inform local proposals. KSMC is applicable when gradients are unknown or prohibitively expensive and inherits the superior performance of SMC on multi-modal targets and its ability to estimate model evidence. Strengths of the proposed methodology are demonstrated on a series of challenging synthetic and real-world examples.