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Inference algorithm

To use a Bayesian network as a classifier, one simply calculates $argmax_yP(y\vert{\bf x})$ using the distribution $P(U)$ represented by the Bayesian network. Now note that

$\displaystyle P(y\vert{\bf x})$ $\textstyle =$ $\displaystyle P(U)/P({\bf x})$  
  $\textstyle \propto$ $\displaystyle P(U)$  
  $\textstyle =$ $\displaystyle \prod_{u\in U}p(u\vert pa(u))%\\
$ (1)

And since all variables in ${\bf x}$ are known, we do not need complicated inference algorithms, but just calculate (1) for all class values.

Remco Bouckaert 2008-05-12