Using Regression for Spectral Estimation of HMMs

 

Hidden Markov Models (HMMs) are widely used to model discrete time series data, but the EM and Gibbs sampling methods used to estimate them are often slow or prone to get stuck in local minima. A more recent class of reduced-dimension spectral methods for estimating HMMs has attractive theoretical properties, but their finite sample size behavior has not been well characterized. We introduce a new spectral model for HMM estimation, a corresponding spectral bilinear regression model, and systematically compare them with a variety of competing simplified models, explaining when and why each method gives superior performance. Using regression to estimate HMMs has a number of advantages, allowing more powerful and flexible modeling.