Beating the Curse of Dimensionality: A Method for High-dimensional Parameter Learning
Authors: Ning Ning, Edward L. Ionides; Published in Journal of Machine Learning Research, Volume 24, Issue 82, Pages 1-76, 2023.
Abstract
Learning parameters in high-dimensional, partially observed, and nonlinear stochastic processes poses significant methodological challenges. One such example is spatiotemporal disease transmission systems, which present open inference problems. In this paper, we propose the iterated block particle filter (IBPF) algorithm for learning high-dimensional parameters in graphical state space models with general state spaces, measures, transition densities, and graph structures. We provide theoretical guarantees on the algorithm’s performance, including overcoming the curse of dimensionality (COD), algorithm convergence, and likelihood maximization. Experimental results on a highly nonlinear and non-Gaussian spatiotemporal model for measles transmission demonstrate the ineffectiveness of the iterated ensemble Kalman filter algorithm (Li et al., 2020) and the curse of dimensionality limitation of the iterated filtering algorithm (Ionides et al., 2015). In contrast, our IBPF algorithm consistently beats COD in various experiments using different metrics.
[Abstract]