Accelerated Inference for Partially Observed Markov Processes using Automatic Differentiation

TL;DR

This paper introduces a new class of algorithms that leverage automatic differentiation for efficient inference in partially observed Markov processes, reducing bias and variance in likelihood estimation.

Contribution

It extends existing AD particle filter methods into a new framework enabling bias-variance tradeoffs and improved mean squared error performance.

Findings

New algorithms outperform existing methods on benchmark problems.

Hybrid AD-based refinement improves inference accuracy.

Requires only a differentiable simulator, not transition probabilities.

Abstract

Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant to AD techniques because widely used particle filter algorithms yield an estimated likelihood function that is discontinuous as a function of the model parameters. We show how to embed two existing AD particle filter methods in a theoretical framework that provides an extension to a new class of algorithms. This new class permits a bias/variance tradeoff and hence a mean squared error substantially lower than the existing algorithms. We develop likelihood maximization algorithms suited to the Monte Carlo properties of the AD gradient estimate. Our algorithms require only a differentiable simulator for the latent dynamic system; by contrast, most previous approaches to AD likelihood maximization for particle filters require access to the system's transition probabilities. Numerical results indicate that a hybrid algorithm that uses AD to refine a coarse solution from an iterated filtering algorithm show substantial improvement on current state-of-the-art methods for a challenging scientific benchmark problem.