Hidden Markov models are powerful models of sequential data which have already been successfully used in several applications, notably speech recognition. They could be applied in many other domains. Many extensions and related models have been proposed in recent years, making such models applicable to an even wider range of learning tasks.
Much research focuses on designing models that better reflect the data, for example trying to remedy the discrepancy between the Markov assumptions (which simplify the mathematics and the algorithms) and the interpretations forced on the state variable (e.g., in speech recognition). In this context, hybrids of HMMs and ANNs and other recent models such as asynchronous Input-Output HMMs are promising but a clear superiority in performance with respect to ordinary HMMs remains to be shown. One of the most interesting aspect of many of these hybrids lies in the simplicity with which different models (such as HMMs and ANNs) can be integrated when they are considered as parametrized devices for transforming numbers into other numbers (which may or may not be part of a probabilistic model). This idea is also important in generalizations of HMMs such as transducers.
Transducers offer a generalization of Markovian models that can be applied to a wide range of learning tasks in which complex a priori structural knowledge about the task is to be smoothly integrated with learning from examples. Local probabilistic assumptions and interpretations of the numbers that are processed by the learning algorithm may be wrong (inconsistent with the data), and the normalization imposed by probabilities may correspond to too strong assumptions about the correct solution. Some of the difficulties inherent in making such probabilistic assumptions and interpretations can be avoided by removing the local probabilistic assumptions and delaying the probabilistic interpretation to the final level of decision.
Acknowledgements The author would like to thank Léon Bottou, Patrick Haffner, Chris Burges, Craig Nohl, Pavel Laskov and Steven Pigeon for their useful comments, as well as the National Sciences and Engineering Research Council of Canada and the Institute of Robotics and Intelligent Systems for their financial support.