“What are Bayesian classifiers?” Bayesian classifiers are statistical classifiers. They can predict class membership probabilities, such as the probability that a given tuple belongs to a particular class.

__Bayesian
Classification__

*“What are Bayesian classifiers?” *Bayesian
classifiers are statistical classifiers. They can* *predict class membership probabilities, such as the probability
that a given tuple belongs to a particular class.

Bayesian
classification is based on Bayes’ theorem, a simple Bayesian classifier known
as the *naïve* *Bayesian classifier *Bayesian classifiers have also exhibited high
accuracy and speed when applied* *to
large databases.

**1. Bayes’ Theorem**

. Let ** X**
be a data tuple. In Bayesian terms,

*“How are these probabilities
estimated?” P*(*H*),* P*(** X**j

**2. Naïve
Bayesian Classification**

**Bayesian
Belief Networks**

.A belief
network is defined by two components—a *directed
acyclic graph* and a set of *conditional
probability tables *(Figure 6.11). Each node in the directed acyclic graph
represents a* *random variable. The
variables may be discrete or continuous-valued. They may correspond to actual
attributes given in the data or to ―hidden variables‖ believed to form a
relationship (e.g., in the case of medical data, a hidden variable may indicate
a syndrome, representing a number of symptoms that, together, characterize a
specific disease). Each arc represents a probabilistic dependence. If an arc is
drawn from a node *Y* to a node *Z*, then *Y* is a parent or immediate predecessor of *Z*, and *Z* is a descendant of
*Y*. *Each variable is conditionally independent of its non* *descendants in the graph, given its parents.*

A belief
network has one conditional probability table (CPT) for each variable. The CPT
for a variable *Y* specifies the
conditional distribution *P*(*Y*j*Parents*(*Y*)), where *Parents*(*Y*) are the
parents of *Y*. Figure(b) shows a CPT
for the variable *LungCancer*. The
conditional probability for each known value of *LungCancer* is given for each possible combination of values of its
parents. For instance, from the upper leftmost and bottom rightmost entries,
respectively, we see that

Let ** X**
= (

following
equation:

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Data Warehousing and Data Mining : Association Rule Mining and Classification : Bayesian Classification |

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