Monte Carlo Hidden Markov Models
Joint work with John Langford and Dieter Fox.
I will present a learning algorithm for hidden Markov models with continuous
state and observation spaces. All necessary probability densities are
approximated using samples, along with density trees generated from such
samples. A Monte Carlo version of Baum-Welch (EM) is employed to learn models
from data, just as in regular HMM learning. Regularization during learning is
achieved using an exponential shrinking technique. The shrinkage factor, which
determines the effective capacity of the learning algorithm, is annealed down
over multiple iterations of Baum-Welch, and early stopping is applied to select
the right model. I will show under mild assumptions, Monte Carlo Hidden Markov
Models converge to a local maximum in likelihood space, just like conventional
HMMs. In addition, I will provide empirical results obtained in a gesture
recognition domain.