Kernel embedding of maps for sequential Bayesian inference: The variational mapping particle filter

• DOI: 10.48550/arxiv.1805.11380
• Publication Date: 2018-01-01
• Authors: Manuel Pulido; Peter Jan vanLeeuwen
• Keywords: Kernel (algebra)

In this work, a novel sequential Monte Carlo filter is introduced which aims at efficient sampling of high-dimensional state spaces with limited number particles. Particles are pushed forward from the prior to posterior density using sequence mappings that minimizes Kullback-Leibler divergence between and intermediate densities. The represents gradient flow. A key ingredient they embedded in reproducing kernel Hilbert space, allows for practical algorithm. embedding provides direct means calculate leading quick convergence well-known gradient-based stochastic optimization algorithms. Evaluation method conducted chaotic Lorenz-63 system, Lorenz-96 coarse prototype atmospheric dynamics, an epidemic model describes cholera dynamics. No resampling required mapping particle even long recursive sequences. effective particles remains close total all experiments.