Model reduction for Hidden Markov models

The contribution of this thesis is the development of tractable computational methods for reducing the complexity of two classes of dynamical systems, finite alphabet Hidden Markov Models and Jump Linear Systems with finite parameter space. The reduction algorithms employ convex optimization and numerical linear algebra tools and do not pose any structural requirements on the systems at hand. In the Jump Linear Systems case, a distance metric based on randomization of the parametric input is introduced. The main point of the reduction algorithm lies in the formulation of two dissipation inequalities, which in conjunction with a suitably defined storage function enable the derivation of low complexity models, whose fidelity is controlled by a guaranteed upper bound on the stochastic L2 gain of the approximation error. The developed reduction procedure can be interpreted as an extension of the balanced truncation method to the broader class of Jump Linear Systems. In the Hidden Markov Model case, Hidden Markov Models are identified with appropriate Jump Linear Systems that satisfy certain constraints on the coefficients of the linear transformation. This correspondence enables the development of a two step reduction procedure.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Kotsalis, Georgios

Advisor dc:contributor.advisor

• Munther A. Dahleh and Alexandre Megretski.

• Mechanical Engineering.

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/1721.1/38255

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/38255