Gradient Ascent Training of BBN

• Let denote a single entry in one of the conditional probability tables. Specifically that variable will take on the value given that its parents take on the values .
• If is the top right entry, then is the variable , is the tuple of parents , and .
• The derivative for each is
• So back to our example we must calculate for each training example in . If the required probability is unobservable then we can calculate it from other variables using standard BBN inference.
• As weights are updated they must remain in the interval [0,1] and the sum remains 1 for all . So must have a two step process
  1. 
  2. renormalize the weights
• will converge to a locally maximum likelihood hypothesis for the conditional probabilities in the BBN