Learning Hidden Markov Models from Pairwise Cooccurrences with Application to Topic Modeling
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:20682077, 2018.
Abstract
We present a new algorithm for identifying the transition and emission probabilities of a hidden Markov model (HMM) from the emitted data. Expectationmaximization 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 secondorder output probabilities, but not higherorder ones. We show that if one is only able to obtain a reliable estimate of the pairwise cooccurrence probabilities of the emissions, it is still possible to uniquely identify the HMM if the emission probability is 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 bagofwords model.
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