Iterated Block Particle Filter for High-dimensional Parameter Learning: Beating the Curse of Dimensionality
This addresses a methodological bottleneck for researchers in fields like epidemiology dealing with high-dimensional inference problems, though it appears incremental as an extension of particle filtering methods.
The authors tackled the challenge of parameter learning in high-dimensional, partially observed, nonlinear stochastic processes, such as spatiotemporal disease transmission, by proposing the iterated block particle filter (IBPF) algorithm, which consistently beats the curse of dimensionality in experiments on a measles transmission model.
Parameter learning for high-dimensional, partially observed, and nonlinear stochastic processes is a methodological challenge. Spatiotemporal disease transmission systems provide examples of such processes giving rise to open inference problems. We propose the iterated 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.