Graphical model: Difference between revisions

Revision as of 02:10, 1 February 2024

Revision as of 16:56, 16 December 2024

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[[File:Examples of an Undirected Graph.svg|thumb|alt=An undirected graph with four vertices.|An undirected graph with four vertices.]]

The undirected graph shown may have one of several interpretations; the common feature is that the presence of an edge implies some sort of dependence between the corresponding random variables. From this graph, we might deduce that <math>B, C, and D</math> are all mutuallyconditionally independent, oncegiven A. This means that if the value of <math>A</math> is known, orthen (equivalentlythe values of B, C, and D provide no further information about each other. Equivalently (in this case), thatthe joint probability distribution can be factorized as:

:<math>P[A,B,C,D] = f_{AB}[A,B] \cdot f_{AC}[A,C] \cdot f_{AD}[A,D]</math>

for some non-negative functions <math>f_{AB}, f_{AC}, f_{AD}</math>.

===Bayesian network===