Spectral dimensionality reduction for HMMs
This provides a faster and more scalable alternative to traditional methods like EM for practitioners in fields using HMMs, though it appears incremental as it builds on existing spectral approaches.
The paper tackles the problem of approximating Hidden Markov Models (HMMs) more efficiently by introducing a spectral method that reduces parameter estimation and achieves sample complexity independent of observation vocabulary size, with proven bounds on probability estimate accuracy.
Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a new spectral method which significantly reduces the number of model parameters that need to be estimated, and generates a sample complexity that does not depend on the size of the observation vocabulary. We present an elementary proof giving bounds on the relative accuracy of probability estimates from our model. (Correlaries show our bounds can be weakened to provide either L1 bounds or KL bounds which provide easier direct comparisons to previous work.) Our theorem uses conditions that are checkable from the data, instead of putting conditions on the unobservable Markov transition matrix.