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Modeling Pixel Means and Covariances Using Factorized ThirdOrder Boltzmann Machines
, 2010
"... Learning a generative model of natural images is a useful way of extracting features that capture interesting regularities. Previous work on learning such models has focused on methods in which the latent features are used to determine the mean and variance of each pixel independently, or on methods ..."
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Cited by 75 (2 self)
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Learning a generative model of natural images is a useful way of extracting features that capture interesting regularities. Previous work on learning such models has focused on methods in which the latent features are used to determine the mean and variance of each pixel independently, or on methods in which the hidden units determine the covariance matrix of a zeromean Gaussian distribution. In this work, we propose a probabilistic model that combines these two approaches into a single framework. We represent each image using one set of binary latent features that model the imagespecific covariance and a separate set that model the mean. We show that this approach provides a probabilistic framework for the widely used simplecell complexcell architecture, it produces very realistic samples of natural images and it extracts features that yield stateoftheart recognition accuracy on the challenging CIFAR 10 dataset.
Learning to combine foveal glimpses with a thirdorder Boltzmann machine
"... We describe a model based on a Boltzmann machine with thirdorder connections that can learn how to accumulate information about a shape over several fixations. The model uses a retina that only has enough high resolution pixels to cover a small area of the image, so it must decide on a sequence of ..."
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Cited by 34 (3 self)
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We describe a model based on a Boltzmann machine with thirdorder connections that can learn how to accumulate information about a shape over several fixations. The model uses a retina that only has enough high resolution pixels to cover a small area of the image, so it must decide on a sequence
HigherOrder Boltzmann Machines
 Neural Networks for Computing
, 1986
"... The Boltzmann machine is a nonlinear network of stochastic binary processing units that interact pairwise through symmetric connection strengths. In a thirdorder Boltzmann machine, triples of units interact through symmetric conjunctive interactions. The Boltzmann learning algorithm is generalized ..."
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Cited by 25 (0 self)
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The Boltzmann machine is a nonlinear network of stochastic binary processing units that interact pairwise through symmetric connection strengths. In a thirdorder Boltzmann machine, triples of units interact through symmetric conjunctive interactions. The Boltzmann learning algorithm is generalized
Subspace Restricted Boltzmann Machine
"... The subspace Restricted Boltzmann Machine (subspaceRBM) is a thirdorder Boltzmann machine where multiplicative interactions are between one visible and two hidden units. There are two kinds of hidden units, namely, gate units and subspace units. The subspace units reflect variations of a pattern in ..."
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The subspace Restricted Boltzmann Machine (subspaceRBM) is a thirdorder Boltzmann machine where multiplicative interactions are between one visible and two hidden units. There are two kinds of hidden units, namely, gate units and subspace units. The subspace units reflect variations of a pattern
A learning algorithm for Boltzmann machines
 Cognitive Science
, 1985
"... The computotionol power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections con allow a significant fraction of the knowledge of the system to be applied to an instance of a probl ..."
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Cited by 584 (13 self)
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The computotionol power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections con allow a significant fraction of the knowledge of the system to be applied to an instance of a problem in o very short time. One kind of computation for which massively porollel networks appear to be well suited is large constraint satisfaction searches, but to use the connections efficiently two conditions must be met: First, a search technique that is suitable for parallel networks must be found. Second, there must be some way of choosing internal representations which allow the preexisting hardware connections to be used efficiently for encoding the constraints in the domain being searched. We describe a generol parallel search method, based on statistical mechanics, and we show how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge obout o task domain in on efficient way. We describe some simple examples in which the learning algorithm creates internal representations thot ore demonstrobly the most efficient way of using the preexisting connectivity structure. 1.
Implicit Mixtures of Restricted Boltzmann Machines
"... We present a mixture model whose components are Restricted Boltzmann Machines (RBMs). This possibility has not been considered before because computing the partition function of an RBM is intractable, which appears to make learning a mixture of RBMs intractable as well. Surprisingly, when formulated ..."
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Cited by 23 (7 self)
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formulated as a thirdorder Boltzmann machine, such a mixture model can be learned tractably using contrastive divergence. The energy function of the model captures threeway interactions among visible units, hidden units, and a single hidden discrete variable that represents the cluster label
Boltzmann machines
, 2007
"... A Boltzmann Machine is a network of symmetrically connected, neuronlike units that make stochastic decisions about whether to be on or off. Boltzmann machines have a simple learning algorithm that allows them to discover interesting features in datasets composed of binary vectors. The learning algor ..."
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Cited by 228 (21 self)
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A Boltzmann Machine is a network of symmetrically connected, neuronlike units that make stochastic decisions about whether to be on or off. Boltzmann machines have a simple learning algorithm that allows them to discover interesting features in datasets composed of binary vectors. The learning
Modeling image structure with factorized phasecoupled Boltzmann machines. arXiv:1011.4058v1
, 2010
"... We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized thirdorder Boltzmann machine that was shown to be effective at capturing higherorder structure in images by modeling dep ..."
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Cited by 1 (1 self)
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We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized thirdorder Boltzmann machine that was shown to be effective at capturing higherorder structure in images by modeling
3d object recognition with deep belief nets
 Advances in Neural Information Processing Systems 22
, 2009
"... We introduce a new type of toplevel model for Deep Belief Nets and evaluate it on a 3D object recognition task. The toplevel model is a thirdorder Boltzmann machine, trained using a hybrid algorithm that combines both generative and discriminative gradients. Performance is evaluated on the NORB d ..."
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Cited by 63 (8 self)
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We introduce a new type of toplevel model for Deep Belief Nets and evaluate it on a 3D object recognition task. The toplevel model is a thirdorder Boltzmann machine, trained using a hybrid algorithm that combines both generative and discriminative gradients. Performance is evaluated on the NORB
Restricted Boltzmann machines for collaborative filtering
 In Machine Learning, Proceedings of the Twentyfourth International Conference (ICML 2004). ACM
, 2007
"... Most of the existing approaches to collaborative filtering cannot handle very large data sets. In this paper we show how a class of twolayer undirected graphical models, called Restricted Boltzmann Machines (RBM’s), can be used to model tabular data, such as user’s ratings of movies. We present eff ..."
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Cited by 220 (12 self)
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Most of the existing approaches to collaborative filtering cannot handle very large data sets. In this paper we show how a class of twolayer undirected graphical models, called Restricted Boltzmann Machines (RBM’s), can be used to model tabular data, such as user’s ratings of movies. We present
Results 1  10
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