Bayesian nonparametric learning of complex dynamical phenomena

The complexity of many dynamical phenomena precludes the use of linear models for which exact analytic techniques are available. However, inference on standard nonlinear models quickly becomes intractable. In some cases, Markov switching processes, with switches between a set of simpler models, are employed to describe the observed dynamics. Such models typically rely on pre-specifying the number of Markov modes. In this thesis, we instead take a Bayesian nonparametric approach in defining a prior on the model parameters that allows for flexibility in the complexity of the learned model and for development of efficient inference algorithms. We start by considering dynamical phenomena that can be well-modeled as a hidden discrete Markov process, but in which there is uncertainty about the cardinality of the state space. The standard finite state hidden Markov model (HMM) has been widely applied in speech recognition, digital communications, and bioinformatics, amongst other fields. Through the use of the hierarchical Dirichlet process (HDP), one can examine an HMM with an unbounded number of possible states. We revisit this HDPHMM and develop a generalization of the model, the sticky HDP-HMM, that allows more robust learning of smoothly varying state dynamics through a learned bias towards self-transitions. We show that this sticky HDP-HMM not only better segments data according to the underlying state sequence, but also improves the predictive performance of the learned model. Additionally, the sticky HDP-HMM enables learning more complex, multimodal emission distributions.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Fox, Emily Beth

Advisor dc:contributor.advisor

• Alan S. Willsky and John W. Fisher, III.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/55111

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/55111