Evaluation of Spectral Learning for the Identification of Hidden Markov Models
This work addresses the problem of parameter estimation for hidden Markov models, which is incremental as it assesses an existing method without introducing new improvements.
The paper evaluated a spectral learning algorithm for identifying hidden Markov models and compared it to expectation-maximization on numerical examples, finding mixed performance with success in some cases with few observations but failure in others even with many observations.
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.