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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Variable elimination ： ウィキペディア英語版 Variable elimination Variable elimination (VE) is a simple and general exact inference algorithm in probabilistic graphical models, such as Bayesian networks and Markov random fields.〔Zhang, N.L., Poole, D.: A Simple Approach to Bayesian Network Computations. In:7th Canadian Conference on Artificial Intelligence, pp. 171–178. Springer, New York(1994)〕〔Zhang, N.L., Poole, D.:A Simple Approach to Bayesian Network Computations.In: 7th Canadian Conference on Artificial Intelligence,pp. 171--178. Springer, New York (1994)〕 It can be used for inference of maximum a posteriori (MAP) state or estimation of marginal distribution over a subset of variables. The algorithm has exponential time complexity, but could be efficient in practice for the low-treewidth graphs, if the proper elimination order is used. ==Inference== The most common query type is in the form $p(X|E\; =\; e)$ where $X$ and $E$ are disjoint subsets of $U$, and $E$ is observed taking value $e$. A basic algorithm to computing p(X|E = e) is called ''variable elimination'' (VE), first put forth in.〔 Algorithm 1, called sum-out (SO), eliminates a single variable $v$ from a set $\backslash phi$ of potentials,〔Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge, MA (2009)〕 and returns the resulting set of potentials. The algorithm collect-relevant simply returns those potentials in $\backslash phi$ involving variable $v$. Algorithm 1 sum-out($v$,$\backslash phi$) :$\backslash Phi$ = collect-relevant($v$,$\backslash phi$) :$\backslash Psi$ = the product of all potentials in $\backslash Phi$ :$\backslash tau\; =\; \backslash sum\_\; \backslash Psi$ return $(\backslash phi\; -\; \backslash Psi)\; \backslash cup\; \backslash$ Algorithm 2, taken from,〔 computes $p(X|E\; =\; e)$ from a discrete Bayesian network B. VE calls SO to eliminate variables one by one. More specifically, in Algorithm 2, $\backslash phi$ is the set C of CPTs for B, $X$ is a list of query variables, $E$is a list of observed variables, $e$ is the corresponding list of observed values, and $\backslash sigma$ is an elimination ordering for variables $U\; -\; XE$, where $XE$ denotes $X\; \backslash cup\; E$. Algorithm 2 VE($\backslash phi,\; X,\; E,\; e,\; \backslash sigma$) :Multiply evidence potentials with appropriate CPTs While σ is not empty :Remove the first variable $v$ from $\backslash sigma$ :$\backslash phi$ = sum-out$(v,\backslash phi)$ :$p(X,\; E\; =\; e)$ = the product of all potentials $\backslash Psi\; \backslash in\; \backslash phi$ return $p(X,E\; =\; e)/\; \backslash sum\_\; p(X,E\; =\; e)$ 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「Variable elimination」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.