Accelerate iterated filtering

TL;DR

This paper introduces an accelerated version of iterated filtering for parameter estimation in partially observed Markov process models, achieving faster convergence and improved performance over previous methods.

Contribution

It presents a novel accelerated iterated filtering algorithm that enhances convergence rates and applies to both convex and non-convex likelihood functions.

Findings

Outperforms previous methods in toy examples

Achieves high convergence rate with relaxed conditions

Effective in modeling infectious diseases

Abstract

In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been introduced and it has been shown that the gradient of the log likelihood can also be approximated. Consequently, different stochastic optimization algorithm can be applied to estimate the parameters of the underlying models. As accelerated gradient is an efficient approach in the optimization literature, we show that we can accelerate iterated filtering in the same manner and inherit that high convergence rate while relaxing the restricted conditions of unbiased gradient approximation. We show that this novel algorithm can be applied to both convex and non-convex log likelihood functions. In addition, this approach has substantially outperformed most of other previous approaches in a toy example and in a challenging scientific problem of modeling infectious diseases.