Evaluation of Spectral Learning for the Identification of Hidden Markov Models

TL;DR

This paper evaluates a spectral learning method for Hidden Markov Model identification, comparing it to traditional expectation-maximization, and finds mixed results with success in some cases but failure in others, possibly due to parameter conditioning.

Contribution

It provides a performance comparison of a spectral subspace-like approach against EM for HMM parameter estimation, highlighting its strengths and limitations.

Findings

Spectral method works well with few observations for some systems.

It fails for certain systems even with many observations.

Performance may depend on system parameter conditioning.

Abstract

Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods, such as maximum-likelihood estimation and especially expectation-maximization, are iterative and prone to have problems with local minima. A non-iterative method employing a spectral subspace-like approach has recently been proposed in the machine learning literature. This paper evaluates the performance of this algorithm, and compares it to the performance of the expectation-maximization algorithm, on a number of numerical examples. We find that the performance is mixed; it successfully identifies some systems with relatively few available observations, but fails completely for some systems even when a large amount of observations is available. An open question is how this discrepancy can be explained. We provide some indications that it could be related to how well-conditioned some system parameters are.