Directed graphical models

for some functions f and g. Probabilistic graphical models are a way of representing conditional independence assumptions using graphs. Nodes represent random variables and lack of edges represent conditional independence assumptions, in a way which we will define below. There are many kinds of graphical model, but the two most popular are Bayesian (belief) networks1, which are based on directed acylic graphs (DAGs), and Markov networks, aka Markov random fields (MRFs), which are based on undirected graphs. In a directed graphical model (DGM), we can (informally) think of an edge from node Xi to node Xj as meaning Xi “causes” or “directly influences” Xj , whereas in an MRF, edges represent correlation rather than causation. In this chapter, we focus on directed graphs.