Distribution learning

Once the network structure is learned, you can choose how to learn the probability tables selecting a class in the weka.classifiers.bayes.net.estimate package.

The SimpleEstimator class produces direct estimates of the conditional probabilities, that is,

$$P(x_i=k\vert pa(x_i)=j)=\frac{N_{ijk}+N_{ijk}'}{N_{ij}+N_{ij}'}$$

where $N_{ijk}'$ is the alpha parameter that can be set and is $0.5$ by default. With $alpha=0$, we get maximum likelihood estimates.

With the BMAEstimator, we get estimates for the conditional probability tables based on Bayes model averaging of all network structures that are substructures of the network structure learned [1]. This is achieved by estimating the conditional probability table of a node $x_i$ given its parents $pa(x_i)$ as a weighted average of all conditional probability tables of $x_i$ given subsets of $pa(x_i)$. The weight of a distribution $P(x_i\vert S)$ with $S\subseteq pa(x_i)$ used is proportional to the contribution of network structure $\forall_{y\in S}y\to x_i$ to either the BDe metric or K2 metric depending on the setting of the useK2Prior option (false and true respectively).