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293
A fast learning algorithm for deep belief nets
 Neural Computation
, 2006
"... We show how to use “complementary priors ” to eliminate the explaining away effects that make inference difficult in denselyconnected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a ..."
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Cited by 930 (51 self)
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We show how to use “complementary priors ” to eliminate the explaining away effects that make inference difficult in denselyconnected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. The fast, greedy algorithm is used to initialize a slower learning procedure that finetunes the weights using a contrastive version of the wakesleep algorithm. After finetuning, a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels. This generative model gives better digit classification than the best discriminative learning algorithms. The lowdimensional manifolds on which the digits lie are modelled by long ravines in the freeenergy landscape of the toplevel associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind. 1
Robust object recognition with cortexlike mechanisms
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2007
"... Abstract—We introduce a new general framework for the recognition of complex visual scenes, which is motivated by biology: We describe a hierarchical system that closely follows the organization of visual cortex and builds an increasingly complex and invariant feature representation by alternating b ..."
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Cited by 388 (48 self)
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Abstract—We introduce a new general framework for the recognition of complex visual scenes, which is motivated by biology: We describe a hierarchical system that closely follows the organization of visual cortex and builds an increasingly complex and invariant feature representation by alternating between a template matching and a maximum pooling operation. We demonstrate the strength of the approach on a range of recognition tasks: From invariant single object recognition in clutter to multiclass categorization problems and complex scene understanding tasks that rely on the recognition of both shapebased as well as texturebased objects. Given the biological constraints that the system had to satisfy, the approach performs surprisingly well: It has the capability of learning from only a few training examples and competes with stateoftheart systems. We also discuss the existence of a universal, redundant dictionary of features that could handle the recognition of most object categories. In addition to its relevance for computer vision, the success of this approach suggests a plausibility proof for a class of feedforward models of object recognition in cortex.
Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations
 IN ICML’09
, 2009
"... ..."
PAMPAS: RealValued Graphical Models for Computer Vision
, 2003
"... Probabilistic models have been adopted for many computer vision applications, however inference in highdimensional spaces remains problematic. As the statespace of a model grows, the dependencies between the dimensions lead to an exponential growth in computation when performing inference. Many comm ..."
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Cited by 120 (3 self)
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Probabilistic models have been adopted for many computer vision applications, however inference in highdimensional spaces remains problematic. As the statespace of a model grows, the dependencies between the dimensions lead to an exponential growth in computation when performing inference. Many common computer vision problems naturally map onto the graphical model framework; the representation is a graph where each node contains a portion of the statespace and there is an edge between two nodes only if they are not independent conditional on the other nodes in the graph. When this graph is sparsely connected, belief propagation algorithms can turn an exponential inference computation into one which is linear in the size of the graph. However belief propagation is only applicable when the variables in the nodes are discretevalued or jointly represented by a single multivariate Gaussian distribution, and this rules out many computer vision applications.
A hierarchical Bayesian model of invariant pattern recognition in the visual cortex
 In Proceedings of the International Joint Conference on Neural Networks. IEEE
, 2005
"... Abstract — We describe a hierarchical model of invariant visual pattern recognition in the visual cortex. In this model, the knowledge of how patterns change when objects move is learned and encapsulated in terms of high probability sequences at each level of the hierarchy. Configuration of object p ..."
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Cited by 69 (2 self)
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Abstract — We describe a hierarchical model of invariant visual pattern recognition in the visual cortex. In this model, the knowledge of how patterns change when objects move is learned and encapsulated in terms of high probability sequences at each level of the hierarchy. Configuration of object parts is captured by the patterns of coincident high probability sequences. This knowledge is then encoded in a highly efficient Bayesian Network structure.The learning algorithm uses a temporal stability criterion to discover object concepts and movement patterns. We show that the architecture and algorithms are biologically plausible. The large scale architecture of the system matches the large scale organization of the cortex and the microcircuits derived from the local computations match the anatomical data on cortical circuits. The system exhibits invariance across a wide variety of transformations and is robust in the presence of noise. Moreover, the model also offers alternative explanations for various known cortical phenomena. I.
Towards a mathematical theory of cortical microcircuits. PLoS computational biology 5
, 2009
"... The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatiotemporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathema ..."
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Cited by 64 (0 self)
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The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatiotemporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is abstracted using a coincidence detector and a mixture of Markov chains. Bayesian belief propagation equations for such an HTM node define a set of functional constraints for a neuronal implementation. Anatomical data provide a contrasting set of organizational constraints. The combination of these two constraints suggests a theoretically derived interpretation for many anatomical and physiological features and predicts several others. We describe the pattern recognition capabilities of HTM networks and demonstrate the application of the derived circuits for modeling the subjective contour effect. We also discuss how the theory and the circuit can be extended to explain cortical features that are not explained by the current model and describe testable predictions that can be derived from the model.
A probabilistic framework for 3D visual object representation: Experimental data,” 2009. [Online]. Available: http://intelsig.org/publications/Detry2009PAMI/ Renaud Detry earned his engineering degree at the University of Liège in 2006. He is currently
 University of Massachusetts
, 2009
"... Abstract—We present an object representation framework that encodes probabilistic spatial relations between 3D features and organizes these features in a hierarchy. Features at the bottom of the hierarchy are bound to local 3D descriptors. Higherlevel features recursively encode probabilistic spati ..."
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Cited by 46 (24 self)
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Abstract—We present an object representation framework that encodes probabilistic spatial relations between 3D features and organizes these features in a hierarchy. Features at the bottom of the hierarchy are bound to local 3D descriptors. Higherlevel features recursively encode probabilistic spatial configurations of more elementary features. The hierarchy is implemented in a Markov network. Detection is carried out by a belief propagation algorithm, which infers the pose of highlevel features from local evidence and reinforces local evidence from globally consistent knowledge, effectively producing a likelihood for the pose of the object in the detection scene. We also present a simple learning algorithm that autonomously builds hierarchies from local object descriptors. We explain how to use our framework to estimate the pose of a known object in an unknown scene. Experiments demonstrate the robustness of hierarchies to input noise, viewpoint changes and occlusions. Index Terms—Computer vision, 3D object representation, pose estimation, Nonparametric Belief Propagation. F 1
Hierarchical models in the brain
 PLoS Computational Biology
, 2008
"... This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of statespace or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of a ..."
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Cited by 46 (9 self)
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This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of statespace or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear timeseries analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain.
W (2011) Neural dynamics as sampling: A model for stochastic computation in recurrent networks of spiking neurons. PLoS Comput Biol 7: e1002211
"... The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trialtotrial variability of neural systems in the brain. In principle there ex ..."
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Cited by 37 (4 self)
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The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trialtotrial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on nonreversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical
Functional and Effective Connectivity: A Review
"... Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain’s functional architecture and operational princip ..."
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Cited by 36 (2 self)
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Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain’s functional architecture and operational principles. The inception of this journal has been foreshadowed by an everincreasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead. Key words: causal modeling; brain connectivity; effective connectivity; functional connectivity