Learning Hidden Markov Models from Pairwise Co-occurrences with Application to Topic Modeling
This addresses computational bottlenecks in HMM identification for large datasets, with applications in topic modeling for text analysis.
The paper tackles the problem of learning hidden Markov models (HMMs) from data when only pairwise co-occurrence probabilities are reliably estimable, showing that unique identification is possible under a sufficiently scattered emission condition. It applies this method to topic modeling, demonstrating higher-quality topic learning compared to bag-of-words models.
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.