Graphical model: Difference between revisions

Revision as of 00:11, 2 May 2019

Revision as of 00:36, 2 May 2019

Line 25:

If the network structure of the model is a [[directed acyclic graph]], the model represents a factorization of the joint [[probability]] of all random variables. More precisely, if the events are <math>X_1,\ldots,X_n</math> then the joint probability satisfies

:<math>P[X_1,\ldots,X_n]=\prod_{i=1}^nP[X_i|\text{parentspa}(X_i)]</math>

where <math>\text{parentspa}(X_i)</math> is the set of parents of node <math>X_i</math> (nodes with edges directed towards <math>X_i</math>). In other words, the [[joint distribution]] factors into a product of conditional distributions. For example, the graphical model in the Figure shown above (which is actually not a directed acyclic graph, but an [[ancestral graph]]) consists of the random variables <math>A, B, C, D</math>

with a joint probability density that factors as