Decayed MCMC Filtering
Bhaskara Marthi, Hanna Pasula, Stuart Russell, Yuval Peres
Abstract:
Filteringestimating the state of a partially observable Markov process from a sequence of observationsis 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 inversepolynomial 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.
Keywords:
Pages: 319326
PS Link:
PDF Link: /papers/02/p319marthi.pdf
BibTex:
@INPROCEEDINGS{Marthi02,
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 (UAI02)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2002",
PAGES = "319326"
}

