Recognition of facial expressions - Knowledge Based Systems ...

- correctly identify the goals of modeling (e.g., prediction versus explanation versus
exploration)
- identify many possible observations that may be relevant to the problem
- determine what subset of those observations is worthwhile to model
- organize the observations into variables having mutually exclusive and
collectively exhaustive states
In the next phase of Bayesian-network construction, a directed acyclic graph was created
for encoding assertions of conditional independence. One approach for doing so is based
on the following observations. From the chain rule of probability the relation can be
written as:
For every
{ X ,..., X i − 1}
\
i
p(
x)
=
Equation 2
n
∏
i=
1
p(
x
i
| x1 ,..., x i −1)
X there will be some subset Πi
= X ,..., X
i
} such that X
i
and
{
1 −1
1
Πi
are conditionally independent given Π
i
. That is, for any x ,
Equation 3
p( xi
| x ,..., xi
1)
= p(
xi
| π )
1 −
i
Combining the two previous equations, the relation becomes:
Equation 4
n
∏
p( x)
= p(
| π )
i=
1
x i
i
Figure 8. Simple model for facial expression recognition
The variables sets Π ,..., Π ) correspond to the Bayesian-network parents Pa ,..., Pa ) ,
(
1 n
which in turn fully specify the arcs in the network structure S.
(
1 n
Consequently, to determine the structure of a Bayesian network, the proper tasks are
- 34 -