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Discrete Emissions

There are two types of emission probabilities: discrete, for discrete HMMs, and continuous, for continuous HMMs. In the first case, is a discrete variable, and is generally taken to be multinomial. If the model is homogeneous in the output distributions, its parameters are given by a matrix with elements . However, in many applications of interest, is multivariate and continuous. To obtain a discrete distribution, two approaches are common:

  1. perform a vector quantization [&make_named_href('', "node31.html#Gray84","[48]")] in order to map each vector-valued to a discrete value , and use as emission probability, or more generally,
  2. use multiple codebooks [&make_named_href('', "node31.html#Lee89","[49]")], i.e., split the vector variable in sub-vectors which are assumed to be approximately independent, quantize them separately (with maps ), and use
    [0] as emission probability. For example, in many speech recognition systems, represents spectral information at time t, represents changes in the spectrum, represents the local average of the signal energy at time t, and its time derivative.


Yoshua Bengio
Tue Oct 7 08:34:36 EDT 1997