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CRiSM Seminar

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Location: A1.01

Alexey Koloydenko & Juri Lember (Joint Talk), University of Nottingham
Adjusted Viterbi Training for Hidden Markov Models
The Expectation Maximisation (EM) procedure is a principal tool for parameter estimation in hidden Markov models (HMMs). However, in applications EM is sometimes replaced by Viterbi training, or extraction, (VT). VT is computationally less intensive and more stable, and has more of an intuitive appeal, but VT estimation is biased and does not satisfy the following fixed point property: Hypothetically, given an infinitely large sample and initialized to the true parameters, VT will generally move away from the initial values. We propose adjusted Viterbi training (VA), a new method to restore the fixed point property and thus alleviate the overall imprecision of the VT estimators, while preserving the computational advantages of the baseline VT algorithm. Simulations show that VA indeed improves estimation precision appreciably in both the special case of mixture models and more general HMMs.

We will discuss the main idea of the adjusted Viterbi training. This will also touch on tools developed specifically to analyze asymptotic behaviour of maximum a posteriori (MAP) hidden paths, also known as Viterbi alignments. Our VA correction is analytic and relies on infinite Viterbi alignments and associated limiting probability distributions. While explicit in the special case of mixture models, these limiting measures are not obvious to exist for more general HMMs. We will conclude by presenting a result that under certain mild conditions, general (discrete time) HMMs do possess the limiting distributions required for the construction of VA. 

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