MIHMMs: Mutual Information Hidden Markov Models

Approach

Hidden Markov Models are usually trained to maximize the likelihood of the observations and hidden states. That objective gives a good generative model, but it does not directly reward hidden states for being informative about the observations, a useful property in classification and clustering.

Mutual Information Hidden Markov Models (MIHMMs) keep the graphical structure of an HMM but change the training objective to a weighted combination of likelihood and mutual information between observations and hidden states. We derived parameter-estimation equations for discrete and continuous observations, in supervised and unsupervised settings.

Across the synthetic and real classification tasks reported in our paper, MIHMMs outperformed standard maximum-likelihood HMMs. We tested the objective on selected tasks rather than establishing a universal advantage: performance still depended on the data, model structure, and weighting between likelihood and mutual information.

Publications

@inproceedings{oliver2002mihmm,
  author = {Nuria Oliver and Ashutosh Garg},
  title = {{MIHMM}: Mutual Information Hidden {Markov} Models},
  booktitle = {International Conference on Machine Learning (ICML 2002)},
  year = 2002,
  url = {https://www.microsoft.com/en-us/research/publication/mmihmm-maximum-mutual-information-hidden-markov-models/}
}