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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 Restricted Boltzmann machine ： ウィキペディア英語版 Restricted Boltzmann machine A restricted Boltzmann machine (RBM) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs. RBMs were initially invented under the name Harmonium by Paul Smolensky in 1986, but only rose to prominence after Geoffrey Hinton and collaborators invented fast learning algorithms for them in the mid-2000s. RBMs have found applications in dimensionality reduction, classification, collaborative filtering, feature learning and topic modelling.〔Ruslan Salakhutdinov and Geoffrey Hinton (2010). (Replicated softmax: an undirected topic model ). ''Neural Information Processing Systems'' 23.〕 They can be trained in either supervised or unsupervised ways, depending on the task. As their name implies, RBMs are a variant of Boltzmann machines, with the restriction that their neurons must form a bipartite graph: a pair of nodes from each of the two groups of units, commonly referred to as the "visible" and "hidden" units respectively, may have a symmetric connection between them, and there are no connections between nodes within a group. By contrast, "unrestricted" Boltzmann machines may have connections between hidden units. This restriction allows for more efficient training algorithms than are available for the general class of Boltzmann machines, in particular the gradient-based contrastive divergence algorithm.〔Miguel Á. Carreira-Perpiñán and Geoffrey Hinton (2005). On contrastive divergence learning. ''Artificial Intelligence and Statistics''.〕 Restricted Boltzmann machines can also be used in deep learning networks. In particular, deep belief networks can be formed by "stacking" RBMs and optionally fine-tuning the resulting deep network with gradient descent and backpropagation. ==Structure== The standard type of RBM has binary-valued (Boolean/Bernoulli) hidden and visible units, and consists of a matrix of weights $W\; =\; (w\_)$ (size ''m''×''n'') associated with the connection between hidden unit $h\_j$ and visible unit $v\_i$, as well as bias weights (offsets) $a\_i$ for the visible units and $b\_j$ for the hidden units. Given these, the ''energy'' of a configuration (pair of boolean vectors) is defined as :$E(v,h)\; =\; -\backslash sum\_i\; a\_i\; v\_i\; -\; \backslash sum\_j\; b\_j\; h\_j\; -\backslash sum\_i\; \backslash sum\_j\; v\_i\; w\_\; h\_j$ or, in matrix notation, :$E(v,h)\; =\; -a^\}\; h\; -v^\; e^$ where $Z$ is a partition function defined as the sum of $e^$ over all possible configurations (in other words, just a normalizing constant to ensure the probability distribution sums to 1). Similarly, the (marginal) probability of a visible (input) vector of booleans is the sum over all possible hidden layer configurations:〔 :$P(v)\; =\; \backslash frac\; \backslash sum\_h\; e^$ Since the RBM has the shape of a bipartite graph, with no intra-layer connections, the hidden unit activations are mutually independent given the visible unit activations and conversely, the visible unit activations are mutually independent given the hidden unit activations.〔 That is, for $m$ visible units and $n$ hidden units, the conditional probability of a configuration of the visible units , given a configuration of the hidden units , is :$P(v|h)\; =\; \backslash prod\_^m\; P(v\_i|h)$. Conversely, the conditional probability of given is :$P(h|v)\; =\; \backslash prod\_^n\; P(h\_j|v)$. The individual activation probabilities are given by :$P(h\_j=1|v)\; =\; \backslash sigma\; \backslash left(b\_j\; +\; \backslash sum\_^m\; w\_\; v\_i\; \backslash right)\backslash ,$ and $\backslash ,P(v\_i=1|h)\; =\; \backslash sigma\; \backslash left(a\_i\; +\; \backslash sum\_^n\; w\_\; h\_j\; \backslash right)$ where $\backslash sigma$ denotes the logistic sigmoid. The visible units of RBM can be multinomial, although the hidden units are Bernoulli. In this case, the logistic function for visible units is replaced by the Softmax function :$P(v\_i^k\; =\; 1|h)\; =\; \backslash frac\; ^k\; h\_j)\}$ where ''K'' is the number of discrete values that the visible values have. They are applied in topic modeling,〔 and recommender systems.〔 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「Restricted Boltzmann machine」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.