Recognition of facial expressions - Knowledge Based Systems ...

For the case that P h ) = P(
h ) , a simplification can be further done by choosing the
(
i
j
Maximum likelihood (ML) hypothesis:
h
ML
= arg
max P(
D / h )
hi ∈ H
i
The Bayesian network is a graphical model that efficiently encodes the joint probability
distribution for a given set of variables.
A Bayesian network for a set of variables X = X ,..., X } consists of a network structure
{ 1 n
S that encodes a set of conditional independence assertions about variables in X , and a
set P of local probability distributions associated with each variable. Together, these
components define the joint probability distribution for X . The network structure S is a
directed acyclic graph. The nodes in S are in one-to-one correspondence with the
variables X . The term
and
pai
to denote the parents of node
those parents.
X
i
is used to denote both the variable and the corresponding node,
X
i
in S as well as the variables corresponding to
Given the structure S, the joint probability distribution for X is given by:
p(
x)
=
Equation 1
n
∏
i=
1
p(
x i
| pa i
)
The local probability distributions P are the distributions corresponding to the terms in
the product of Equation 1. Consequently, the pair (S;P) encodes the joint distribution
p(x).
The probabilities encoded by a Bayesian network may be Bayesian or physical. When
building Bayesian networks from prior knowledge alone, the probabilities will be
Bayesian. When learning these networks from data, the probabilities will be physical (and
their values may be uncertain).
Difficulties are not unique to modeling with Bayesian networks, but rather are common
to most approaches.
As part of the project several tasks had to be fulfilled, such as:
- 33 -