Decayed MCMC Filtering

TL;DR

Decayed MCMC is a stochastic filtering algorithm that uses a time-favoring proposal distribution for efficient state estimation in large or nonlinear systems, with proven bounded convergence time.

Contribution

The paper introduces decayed MCMC, a novel filtering method that favors recent states and provides theoretical convergence guarantees for ergodic processes.

Findings

Convergence time remains bounded as observation sequence length increases.

Decayed MCMC is competitive with particle filtering in experiments.

The algorithm applies a decay-based proposal distribution for improved efficiency.

Abstract

Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior distribution is generally intractable for large discrete systems and for nonlinear continuous systems, so a good deal of effort has gone into developing robust approximation algorithms. This paper describes a simple stochastic approximation algorithm for filtering called {em decayed MCMC}. The algorithm applies Markov chain Monte Carlo sampling to the space of state trajectories using a proposal distribution that favours flips of more recent state variables. The formal analysis of the algorithm involves a generalization of standard coupling arguments for MCMC convergence. We prove that for any ergodic underlying Markov process, the convergence time of decayed MCMC with inverse-polynomial decay remains bounded as the length of the observation sequence grows. We show experimentally that decayed MCMC is at least competitive with other approximation algorithms such as particle filtering.