Estimating the Accuracy of Spectral Learning for HMMs

Hidden Markov models (HMMs) are usually learned using

the expectation maximisation algorithm which is, unfortunately, subject

to local optima. Spectral learning for HMMs provides a unique, optimal

solution subject to availability of a sufficient amount of data. However,

with access to limited data, there is no means of estimating the accuracy

of the solution of a given model. In this paper, a new spectral evaluation

method has been proposed which can be used to assess whether the

algorithm is converging to a stable solution on a given dataset. The

proposed method is designed for real-life datasets where the true model is

not available. A number of empirical experiments on synthetic as well as

real datasets indicate that our criterion is an accurate proxy to measure

quality of models learned using spectral learning.