Evaluation of Spectral Learning for the Identification of Hidden Markov Models

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-iterttive method employing a spectral subspace-like approach has recently been proposed in the machine learning literature. TIC'S 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 Sortie indications that it could be related to how well conditioned sonic system parameters are. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.