Phase transition for parameter learning of Hidden Markov Models
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.
Cite
@article{arxiv.2003.11680,
title = {Phase transition for parameter learning of Hidden Markov Models},
author = {Nikita Rau and Jörg Lücke and Alexander K. Hartmann},
journal= {arXiv preprint arXiv:2003.11680},
year = {2021}
}
Comments
9 pages, 9 figures