Uncertainty in Artificial Intelligence
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Decayed MCMC Filtering
Bhaskara Marthi, Hanna Pasula, Stuart Russell, Yuval Peres
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.
Pages: 319-326
PS Link:
PDF Link: /papers/02/p319-marthi.pdf
AUTHOR = "Bhaskara Marthi and Hanna Pasula and Stuart Russell and Yuval Peres",
TITLE = "Decayed MCMC Filtering",
BOOKTITLE = "Proceedings of the Eighteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-02)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2002",
PAGES = "319--326"

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