Learning Hidden Markov Models from Pairwise Co-occurrences with Application to Topic Modeling

TL;DR

This paper introduces a new algorithm for learning hidden Markov models from pairwise co-occurrence data, enabling more efficient topic modeling when higher-order statistics are unavailable.

Contribution

The authors develop a method to identify HMM parameters using only second-order output probabilities, applicable when data is limited to pairwise co-occurrences.

Findings

Effective HMM parameter estimation from pairwise co-occurrences.

Improved topic modeling quality with shared emission probabilities.

Demonstrated advantages over bag-of-words models.

Abstract

We present a new algorithm for identifying the transition and emission probabilities of a hidden Markov model (HMM) from the emitted data. Expectation-maximization becomes computationally prohibitive for long observation records, which are often required for identification. The new algorithm is particularly suitable for cases where the available sample size is large enough to accurately estimate second-order output probabilities, but not higher-order ones. We show that if one is only able to obtain a reliable estimate of the pairwise co-occurrence probabilities of the emissions, it is still possible to uniquely identify the HMM if the emission probability is \emph{sufficiently scattered}. We apply our method to hidden topic Markov modeling, and demonstrate that we can learn topics with higher quality if documents are modeled as observations of HMMs sharing the same emission (topic) probability, compared to the simple but widely used bag-of-words model.