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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:
- 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,
- 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