Bayes net

A Bayesian network over variables $\{X_1,X_2,\cdots ,X_n\}$ consists of

• A dag (directed acyclic graph) whose nodes are the variables.
  • i.e., we can’t go backwards to a node!
• A set of CPTs (conditional probability tables) $P(X_i|\text{Par}(X_i))$ for each $X_i$.

Some key notions we should think about:

• Parents of a node are denoted $\text{Par}(X_i)$.
• Children, descendants, ancestors of a node.
• Family denotes a set of nodes consisting of $X_i$ and its parents. In Bayes nets, CPTs are defined over families.