Iterated Block Particle Filter for High-dimensional Parameter Learning: Beating the Curse of Dimensionality

Parameter learning for high-dimensional, partially observed, and nonlinear stochastic pro-cesses is a methodological challenge. Spatiotemporal disease transmission systems provide examples of such processes giving rise to open inference problems. We propose the iter-ated block particle filter (IBPF) algorithm for learning high-dimensional parameters over graphical state space models with general state spaces, measures, transition densities and graph structure. Theoretical performance guarantees are obtained on beating the curse of dimensionality (COD), algorithm convergence, and likelihood maximization. Experiments on a highly nonlinear and non-Gaussian spatiotemporal model for measles transmission reveal that the iterated ensemble Kalman filter algorithm (Li et al., 2020) is ineffective and the iterated filtering algorithm (Ionides et al., 2015) suffers from the COD, while our IBPF algorithm beats COD consistently across various experiments with different metrics.

Automated summary

This paper introduces a method for parameter learning in high-dimensional, partially observed, and nonlinear stochastic processes, proposing the iterated block particle filter algorithm. The algorithm shows promising performance in solving the curse of dimensionality in various experiments.