Recognition of facial expressions - Knowledge Based Systems ...

In the final step of constructing a Bayesian network, the local probability distributions
p x i
| pa ) were assessed. In the example, where all variables are discrete, one
(
i
distribution for
are shown in Figure 8.
X
i
was assessed for every configuration of
Inference in a Bayesian Network
Pa
i
. Example distributions
Once a Bayesian network has been constructed (from prior knowledge, data, or a
combination), the next step is to determine various probabilities of interest from the
model. In the problem concerning detection of facial expressions, the probability of the
existence of happiness expression, given observations of the other variables is to be
discovered. This probability is not stored directly in the model, and hence needs to be
computed. In general, the computation of a probability of interest given a model is known
as probabilistic inference. Because a Bayesian network for X determines a joint
probability distribution for X , the Bayesian network was used to compute any probability
of interest. For example, from the Bayesian network in Figure 8, the probability of a
certain expression given observations of the other variables can be computed as follows:
Equation 6
p ( Expression | P , P ,..., P
1
2
10
) =
p(
Expression,
P1
, P2
,..., P
p(
P , P ,..., P )
1
2
10
10
)
=
p(Expression, P1
, P2
,..., P10
)
p(Expression', P , P ,..., P
Expression'
1
2
10
)
For problems with many variables, however, this direct approach is not practical.
Fortunately, at least when all variables are discrete, the conditional independencies can be
exploited encoded in a Bayesian network to make the computation more efficient. In the
example, given the conditional independencies in Equation 5, Equation 6 becomes:
p ( Expression | P , P ,..., P
1
2
10
) =
Expression'
Equation 7
p(Expression)p(P1
| Expression)...p(P10
| Expression)
p(Expression' )p(P | Expression' )...p(P | Expression' )
1
10
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