Stochastic Systems Group  

Reduction of Hidden Markov Models
Munther Dahleh
MIT
In this talk, we first develop a generalization of the balanced truncation algorithm applicable to a special class of discretetime Markov jump linear systems. The approximation error, which is captured by means of the stochastic L2 gain, is bounded from above by twice the sum of singular numbers associated with the truncated states, similar to the case of linear time invariant systems. Then, we propose a two step model reduction algorithm for hidden Markov models. The first step relies on the aforementioned balanced truncation algorithm due to a topological equivalence established between hidden Markov models and a subclass of Markov jump linear systems. The second step enforces the positivity constraints, which reflect the hidden Markov model structure, by solving a low dimensional optimization problem.
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