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arXiv · 2003.11680

Phase transition for parameter learning of Hidden Markov Models

Nikita Rau·Jörg Lücke·Alexander K. Hartmann
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Abstract

We study a phase transition in parameter learning of Hidden Markov Models (HMMs). We do this by generating sequences of observed symbols from given discrete HMMs with uniformly distributed transition probabilities and a noise level encoded in the output probabilities. By using the Baum-Welch (BW) algorithm, an Expectation-Maximization algorithm from the field of Machine Learning, we then try to estimate the parameters of each investigated realization of an HMM. We study HMMs with n=4, 8 and 16 states. By changing the amount of accessible learning data and the noise level, we observe a phase-transition-like change in the performance of the learning algorithm. For bigger HMMs and more learning data, the learning behavior improves tremendously below a certain threshold in the noise strength. For a noise level above the threshold, learning is not possible. Furthermore, we use an overlap parameter applied to the results of a maximum-a-posteriori (Viterbi) algorithm to investigate the accuracy of the hidden state estimation around the phase transition.

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BibTeXRIS

Nikita Rau, Jörg Lücke, Alexander K. Hartmann. 2020-03-25. Phase transition for parameter learning of Hidden Markov Models. https://doi.org/10.1103/physreve.104.044105

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