  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.
