Gradient Ascent for Bayes Nets

Let $w_{ijk}$ denote one entry in the conditional probability table for variable $Y_i$ in the network \[ w_{ijk} = P(Y_i=y_{ij}\,|\,Parents(Y_i) = \text{the list} u_{ik} \text{of values}) \] e.g., if $Y_i = Campfire$, then $u_{ik}$ might be $\langle Storm=T, BusTourGroup=F \rangle$
Perform gradient ascent by repeatedly
1. update all $w_{ijk}$ using training data $D$ \[w_{ijk} \leftarrow w_{ijk} + \eta \sum_{d \in D} \frac{P_h(y_{ij}, u_{ik} \,|\, d)}{w_{ijk}} \]
2. then, re-normalize the $w_{ijk}$ to assure $\sum_{j} w_{ijk} = 1$ and $0 \leq w_{ijk} \leq 1$
If some of the probabilities are not present in the data they can be derived via inference from the net.
Again, this only finds locally optimal conditional probabilities.