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Graphoid
A graphoid is a set of statements of the form, "''X'' is irrelevant to ''Y'' given that we know ''Z''" where ''X'', ''Y'' and ''Z'' are sets of variables. The notion of "irrelevance" and "given that we know" may obtain different interpretations, including probabilistic, relational and correlational, depending on the application. These interpretations share common properties that can be captured by paths in graphs (hence the name "graphoid"). The theory of graphoids characterizes these properties in a finite set of axioms that are common to informational irrelevance and its graphical representations. ==History== Judea Pearl and Azaria Paz coined the term "graphoids" after discovering that a set of axioms that govern conditional independence in probability theory is shared by undirected graphs. Variables are represented as nodes in a graph in such a way that variable sets ''X'' and ''Y'' are independent conditioned on ''Z'' in the distribution whenever node set ''Z'' separates ''X'' from ''Y'' in the graph. Axioms for conditional independence in probability were derived earlier by A. Philip Dawid and Wolfgang Spohn. The correspondence between dependence and graphs was later extended to directed acyclic graphs (DAGs) and to other models of dependency.〔
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Graphoid」の詳細全文を読む
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