Density Ratio Hidden Markov Models

Masashi Sugiyama Department of Computer Science Tokyo Institute of Technology Tokyo 152-8552, Japan sugi@cs.titech.ac.jp Abstract Hidden Markov models and their variants are the predominant sequential classification method in such domains as speech recognition, bioinformatics and natural language processing. Being generative rather than discriminative models, however, their classification performance is a drawback. In this paper we apply ideas from the field of density ratio estimation to bypass the difficult step of learning likelihood functions in HMMs. By reformulating inference and model fitting in terms of density ratios and applying a fast kernel-based estimation method, we show that it is possible to obtain a striking increase in discriminative performance while retaining the probabilistic qualities of the HMM. We demonstrate experimentally that this formulation makes more efficient use of training data than alternative approaches. 1 Introduction Inference of a sequence of estimated classes from a sequence of noisy observations is fundamental in many applications. The hidden Markov model (HMM) and its variants are the usual methods employed to do this, and have been used with conspicuous success in such domains as speech recognition, bioinformatics and natural language processing. As well as being computationally efficient, they are a popular choice due to their intuitive probabilistic interpretation.