1. Graphical Models

2. Intro Models with modest # variables run into computation problems.
What queries are we interested in:
(in) dependencies and condional & marginal probabilities.
A marriage between graph theory and probability theory will
provide the language for this structure.
two flavors: directed & undirected graphical models.
independencies implied by graph  structures prob. distr.

3. Directed Acyclic Graphs
prob. distr. = prod. of local factors
no cycles allowed!
structure: Bayes’ rule, with some dependencies removed
interpretation: causal depencies between parents & children
d-separability.
3 canonical subgraphs  Bayes’ ball algorithm

4. Undirected Graphs Graph separability  undirected graphs
prob. distr. prod of un-normalized factors
factors live on maximal cliques
there are UGM that imply cond. indep. not captures in any DGM, and vice versa.
simplified parametrizations for computational efficiency.