**Compact representation of multivariate probability distributions**

Probabilistic graphical models for a set of variables \(\{ X_1, X_2, \ldots, X_n \}\) characterized by

- a graphical structure, directed and acyclic, whose nodes are the variables
- a probability model for each node describing the relationship with its parents
- edges encode conditional independencies (any variable is conditionally independent of its non-descendant given its parents)