Learning stochastic filtering

TL;DR

This paper evaluates stochastic filtering approximations using Kullback-Leibler divergence, comparing a static filter and machine learning-based Voltera expansions on a Markov process with Brownian measurement, emphasizing the importance of the performance metric.

Contribution

It introduces a framework for quantifying filtering approximation performance and compares traditional and machine learning methods using a specific divergence metric.

Findings

Machine learning Voltera expansions outperform static filters in certain scenarios.

The choice of performance metric significantly impacts filter evaluation.

Two solutions are proposed for likelihood prediction within bounded constraints.

Abstract

We quantify the performance of approximations to stochastic filtering by the Kullback-Leibler divergence to the optimal Bayesian filter. Using a two-state Markov process that drives a Brownian measurement process as prototypical test case, we compare two stochastic filtering approximations: a static low-pass filter as baseline, and machine learning of Voltera expansions using nonlinear Vector Auto Regression (nVAR). We highlight the crucial role of the chosen performance metric, and present two solutions to the specific challenge of predicting a likelihood bounded between $0$ and $1$.