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An influence diagram (ID) (also called a relevance diagram, decision diagram or a decision network) is a compact graphical and mathematical representation of a decision situation. It is a generalization of a Bayesian network, in which not only probabilistic inference problems but also decision making problems (following maximum expected utility criterion) can be modeled and solved. ID was first developed in mid-1970s within the decision analysis community with an intuitive semantic that is easy to understand. It is now adopted widely and becoming an alternative to decision tree which typically suffers from exponential growth in number of branches with each variable modeled. ID is directly applicable in team decision analysis, since it allows incomplete sharing of information among team members to be modeled and solved explicitly. Extension of ID also find its use in game theory as an alternative representation of game tree. ==Semantics== An ID is a directed acyclic graph with three types (plus one subtype) of node and three types of arc (or arrow) between nodes. Nodes; : *''Decision node'' (corresponding to each decision to be made) is drawn as a rectangle. : *''Uncertainty node'' (corresponding to each uncertainty to be modeled) is drawn as an oval. :: *''Deterministic node'' (corresponding to special kind of uncertainty that its outcome is deterministically known whenever the outcome of some other uncertainties are also known) is drawn as a double oval. : *''Value node'' (corresponding to each component of additively separable Von Neumann-Morgenstern utility function) is drawn as an octagon (or diamond). Arcs; : *''Functional arcs'' (ending in value node) indicate that one of the components of additively separable utility function is a function of all the nodes at their tails. : *''Conditional arcs'' (ending in uncertainty node) indicate that the uncertainty at their heads is probabilistically conditioned on all the nodes at their tails. :: *''Conditional arcs'' (ending in deterministic node) indicate that the uncertainty at their heads is deterministically conditioned on all the nodes at their tails. : *''Informational arcs'' (ending in decision node) indicate that the decision at their heads is made with the outcome of all the nodes at their tails known beforehand. Given a properly structured ID; : *Decision nodes and incoming information arcs collectively state the ''alternatives'' (what can be done when the outcome of certain decisions and/or uncertainties are known beforehand) : *Uncertainty/deterministic nodes and incoming conditional arcs collectively model the ''information'' (what are known and their probabilistic/deterministic relationships) : *Value nodes and incoming functional arcs collectively quantify the ''preference'' (how things are preferred over one another). ''Alternative, information, and preference'' are termed ''decision basis'' in decision analysis, they represent three required components of any valid decision situation. Formally, the semantic of influence diagram is based on sequential construction of nodes and arcs, which implies a specification of all conditional independencies in the diagram. The specification is defined by the -separation criterion of Bayesian network. According to this semantic, every node is probabilistically independent on its non-successor nodes given the outcome of its immediate predecessor nodes. Likewise, a missing arc between non-value node and non-value node implies that there exists a set of non-value nodes , e.g., the parents of , that renders independent of given the outcome of the nodes in . 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「Influence diagram」の詳細全文を読む スポンサード リンク
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