Bayes neural networks and its application to estimation of hiddenMarkov chains

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A hidden Markov chain is a sequence of states. Though the states cannot be observed, the signals, each of which is generated accompanying the transition of the states, can be observed. We have tried to estimate the sequence of states using a neural network from the observation. For the estimation, Bayesian discriminant functions are necessary. Our neural network can learn several Bayesian discriminant functions simultaneously if necessary. In the case of low-dimensional signals, the network successfully estimated a hidden Markov chain. The algorithm can in principle be applied to higher-dimensional signal cases.