Recognition of facial expressions - Knowledge Based Systems ...

Several researchers have developed probabilistic inference algorithms for Bayesian
networks with discrete variables that exploit conditional independence. Pearl (1986)
developed a message-passing scheme that updates the probability distributions for each
node in a Bayesian network in response to observations of one or more variables.
Lauritzen and Spiegelhalter (1988), Jensen et al. (1990), and Dawid (1992) created an
algorithm that first transforms the Bayesian network into a tree where each node in the
tree corresponds to a subset of variables in X. The algorithm then exploits several
mathematical properties of this tree to perform probabilistic inference.
The most commonly used algorithm for discrete variables is that of Lauritzen and
Spiegelhalter (1988), Jensen et al (1990), and Dawid (1992). Methods for exact inference
in Bayesian networks that encode multivariate-Gaussian or Gaussianmixture distributions
have been developed by Shachter and Kenley (1989) and Lauritzen (1992), respectively.
Approximate methods for inference in Bayesian networks with other distributions, such
as the generalized linear-regression model, have also been developed (Saul et al., 1996;
Jaakkola and Jordan, 1996). For those applications where generic inference methods are
impractical, researchers are developing techniques that are custom tailored to particular
network topologies (Heckerman 1989; Suermondt and Cooper, 1991; Saul et al., 1996;
Jaakkola and Jordan, 1996) or to particular inference queries (Ramamurthi and Agogino,
1988; Shachter et al., 1990; Jensen and Andersen, 1990; Darwiche and Provan, 1996).
Gradient Ascent for Bayes Nets
If wijk
denote one entry in the conditional probability table for variable Y
i
in the network,
then:
w
ijk
= P(Yi = yij
| Parents(Y
i
) = thelist u
ik
of
values)
Perform gradient ascent by repeatedly performing:
- update all wijk
using training data D
w
ijk
← w
ijk
+ η
d∈D
P
h
( yij,uik
w
ijk
| d)
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