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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 Generalized filtering ： ウィキペディア英語版 Generalized filtering Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models.〔K Friston, K Stephan, B Li, and J. Daunizeau, "(Generalised Filtering )," Mathematical Problems in Engineering, vol. vol., 2010, p. 621670, 2010.〕 It is based on a variational principle of least action, formulated in generalized coordinates of motion.〔B Balaji and K Friston, "(Bayesian state estimation using generalized coordinates )," Proc. SPIE, p. 80501Y , 2011〕 Generalized filtering furnishes posterior densities over hidden states (and parameters) generating observed data using a generalized gradient descent on variational free energy, under the Laplace assumption. Unlike classical (e.g., Kalman-Bucy or particle) filtering, generalized filtering eschews Markovian assumptions about random fluctuations. Furthermore, it operates online, assimilating data to approximate the posterior density over unknown quantities, without the need for a backward pass. Special cases include variational filtering,〔 dynamic expectation maximization〔 and generalized predictive coding. == Definition == Definition: Generalized filtering rests on the tuple $(\backslash Omega,U,X,S,p,q)$: * ''A sample space'' $\backslash Omega$ from which random fluctuations $\backslash omega\; \backslash in\; \backslash Omega$ are drawn * ''Control states'' $U\; \backslash in\; \backslash mathbb$ – that act as external causes, input or forcing terms * ''Hidden states'' $X:X\; \backslash times\; U\; \backslash times\; \backslash Omega\; \backslash to\; \backslash mathbb$ – that cause sensor states and depend on control states * ''Sensor states'' $S:X\; \backslash times\; U\; \backslash times\; \backslash Omega\; \backslash to\; \backslash mathbb$ – a probabilistic mapping from hidden and control states * ''Generative density'' $p(\backslash tilde,\backslash tilde,\backslash tilde\backslash mid\; m)$ – over sensory, hidden and control states under a generative model * ''Variational density'' $q(\backslash tilde,\backslash tilde\backslash mid\; m)$ – over hidden and control states with mean $\backslash tilde\; \backslash in\; \backslash mathbb$ Here ~ denotes a variable in generalized coordinates of motion: $\backslash tilde\; =\; ()^T$ 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「Generalized filtering」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.