Monte Carlo Hidden Markov Models: Learning Non-Parametric Models of Partially Observable Stochastic Processes

We present a learning algorithm for non-parametric 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. 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 BaumWelch, and early stopping is applied to select the right model. Once trained, Monte Carlo HMMs can be run in an any-time fashion. We prove that under mild assumptions, Monte Carlo Hidden Markov Models converge to a local maximum in likelihood space, just like conventional HMMs. In addition, we provide empirical results obtained in a gesture recognition domain.