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Abstract:
We show that it is possible to extend hidden Markov models to
have a countably infinite number of hidden states. By using the
theory of Dirichlet processes we can implicitly integrate out the
infinitely many transition parameters, leaving only three
hyperparameters which can be learned from data. These three
hyperparameters define a hierarchical Dirichlet process capable
of capturing a rich set of transition dynamics. The three
hyperparameters control the time scale of the dynamics, the
sparsity of the underlying state-transition matrix, and the
expected number of distinct hidden states in a finite sequence.
In this framework it is also natural to allow the alphabet of
emitted symbols to be infinite -- consider, for example, symbols
being possible words appearing in English text.
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