Motivation

Want to learn a belief net representation for a domain based on data.

Bayesian Learning: for making predictions.

Compute a weighted sum of predictors:

$$\Pr(X\vert D) = \sum_i \Pr(X\vert H_i) \Pr(H_i\vert D)$$

X is the quantity to be predicted, D the data, and H_i the possible predictors (hypotheses or models).

This is the best possible prediction (assuming we're Bayesians).