Above are papers related to the following paper: [Paper_ID] Paper #66982. 	[Title] Learning Generative Models with the Up-Propagation Algorithm [Abstract] Up-propagation is an algorithm for inverting and learning neural network generative models. Sensory input is processed by inverting a model that generates patterns from hidden variables using top-down connections. The inversion process is iterative, utilizing a negative feedback loop that depends on an error signal propagated by bottom-up connections. The error signal is also used to learn the generative model from examples. The algorithm is benchmarked against principal component analysis in In his doctrine of unconscious inference, Helmholtz argued that perceptions are formed by the interaction of bottom-up sensory data with top-down expectations. According to one interpretation of this doctrine, perception is a procedure of sequential hypothesis testing. We propose a new algorithm, called up-propagation, that realizes this interpretation in layered neural networks. It uses top-down connections to generate hypotheses, and bottom-up connections to revise them. It is important to understand the difference between up-propagation and its ancestor, the backpropagation algorithm[1]. Backpropagation is a learning algorithm for recognition models. As shown in Figure 1a, bottom-up connections recognize patterns, while top-down connections propagate an error signal that is used to learn the recognition model. In contrast, up-propagation is an algorithm for inverting and learning generative models, as shown in Figure 1b. Top-down connections generate patterns from a set of hidden variables. Sensory input is processed by inverting the generative model, recovering hidden variables that could have generated the sensory data. This operation is called either pattern recognition or pattern analysis, depending on the meaning of the hidden variables. Inversion of the generative model is done iteratively, through a negative feedback loop driven by an error signal from the bottom-up connections. The error signal is also used for learning the connections experiments on images of handwritten digits. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152904. 	[Title] GIBBS-MARKOV MODELS [Abstract] In this paper we present a framework for building probabilistic automata parameterized by context-dependent probabilities. Gibbs distributions are used to model state transitions and output generation, and parameter estimation is carried out using an EM algorithm where the M-step uses a generalized iterative scaling procedure. We discuss relations with certain classes of stochastic feedforward neural networks, a geometric interpretation for parameter estimation, and a simple example of a statistical language model constructed using this methodology. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #390922. 	[Title] A MEAN FIELD LEARNING ALGORITHM FOR UNSUPERVISED NEURAL NETWORKS [Abstract] We introduce a learning algorithm for unsupervised neural networks based on ideas from statistical mechanics. The algorithm is derived from a mean field approximation for large, layered sigmoid belief networks. We show how to (approximately) infer the statistics of these networks without resort to sampling. This is done by solving the mean field equations, which relate the statistics of each unit to those of its Markov blanket. Using these statistics as target values, the weights in the network are adapted by a local delta rule. We evaluate the strengths and weaknesses of these networks for problems in statistical pattern recognition. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152272. 	[Title] GIBBS-MARKOV MODELS [Abstract] In this paper we present a framework for building probabilistic automata parameterized by context-dependent probabilities. Gibbs distributions are used to model state transitions and output generation, and parameter estimation is carried out using an EM algorithm where the M-step uses a generalized iterative scaling procedure. We discuss relations with certain classes of stochastic feedforward neural networks, a geometric interpretation for parameter estimation, and a simple example of a statistical language model constructed using this methodology. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #32276. 	[Title] Extracting Support Data for a Given Task [Abstract] We report a novel possibility for extracting a small subset of a data base which contains all the information necessary to solve a given classification task: using the Support Vector Algorithm to train three different types of handwritten digit classifiers, we observed that these types of classifiers construct their decision surface from strongly overlapping small ( 4%) subsets of the data base. This finding opens up the possibility of compressing data bases significantly by disposing of the data which is not important for the solution of a given task. In addition, we show that the theory allows us to predict the classifier that will have the best generalization ability, based solely on performance on the training set and characteristics of the learning machines. This finding is important for cases where the amount of available data is limited. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28957. 	[Title] Operations for Learning with Graphical Models decomposition techniques and the demonstration that graphical models provide [Abstract] This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing how some popular algorithms fall within the framework presented. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3229. 	[Title] Book Review  Introduction to the Theory of Neural Computation Reviewed by: 2 [Abstract] Neural computation, also called connectionism, parallel distributed processing, neural network modeling or brain-style computation, has grown rapidly in the last decade. Despite this explosion, and ultimately because of impressive applications, there has been a dire need for a concise introduction from a theoretical perspective, analyzing the strengths and weaknesses of connectionist approaches and establishing links to other disciplines, such as statistics or control theory. The Introduction to the Theory of Neural Computation by Hertz, Krogh and Palmer (subsequently referred to as HKP) is written from the perspective of physics, the home discipline of the authors. The book fulfills its mission as an introduction for neural network novices, provided that they have some background in calculus, linear algebra, and statistics. It covers a number of models that are often viewed as disjoint. Critical analyses and fruitful comparisons between these models Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #39199. 	[Title] Unsupervised Learning by Convex and Conic Coding [Abstract] Unsupervised learning algorithms based on convex and conic encoders are proposed. The encoders find the closest convex or conic combination of basis vectors to the input. The learning algorithms produce basis vectors that minimize the reconstruction error of the encoders. The convex algorithm develops locally linear models of the input, while the conic algorithm discovers features. Both algorithms are used to model handwritten digits and compared with vector quantization and principal component analysis. The neural network implementations involve feedback connections that project a reconstruction back to the input layer. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #50336. 	[Title] Computing upper and lower bounds on likelihoods in intractable networks [Abstract] We present deterministic techniques for computing upper and lower bounds on marginal probabilities in sigmoid and noisy-OR networks. These techniques become useful when the size of the network (or clique size) precludes exact computations. We illustrate the tightness of the bounds by numerical experi ments. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #50337. 	[Title] Recursive algorithms for approximating probabilities in graphical models [Abstract] MIT Computational Cognitive Science Technical Report 9604 Abstract We develop a recursive node-elimination formalism for efficiently approximating large probabilistic networks. No constraints are set on the network topologies. Yet the formalism can be straightforwardly integrated with exact methods whenever they are/become applicable. The approximations we use are controlled: they maintain consistently upper and lower bounds on the desired quantities at all times. We show that Boltzmann machines, sigmoid belief networks, or any combination (i.e., chain graphs) can be handled within the same framework. The accuracy of the methods is verified exper imentally. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152162. 	[Title] GIBBS-MARKOV MODELS [Abstract] In this paper we present a framework for building probabilistic automata parameterized by context-dependent probabilities. Gibbs distributions are used to model state transitions and output generation, and parameter estimation is carried out using an EM algorithm where the M-step uses a generalized iterative scaling procedure. We discuss relations with certain classes of stochastic feedforward neural networks, a geometric interpretation for parameter estimation, and a simple example of a statistical language model constructed using this methodology. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #52515. 	[Title] Unsupervised learning of distributions on binary vectors using two layer networks [Abstract] We present a distribution model for binary vectors, called the influence combination model and show how this model can be used as the basis for unsupervised learning algorithms for feature selection. The model is closely related to the Harmonium model defined by Smolensky [RM86][Ch.6]. In the first part of the paper we analyze properties of this distribution representation scheme. We show that arbitrary distributions of binary vectors can be approximated by the combination model. We show how the weight vectors in the model can be interpreted as high order correlation patterns among the input bits. We compare the combination model with the mixture model and with principle component analysis. In the second part of the paper we present two algorithms for learning the combination model from examples. The first algorithm is based on gradient ascent. Here we give a closed form for this gradient that is significantly easier to compute than the corresponding gradient for the general Boltzmann machine. The second learning algorithm is a greedy method that creates the hidden units and computes their weights one at a time. This method is a variant of projection pursuit density estimation. In the third part of the paper we give experimental results for these learning methods on synthetic data and on natural data of handwritten digit images. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #39210. 	[Title] Pattern analysis and synthesis in attractor neural networks [Abstract] The representation of hidden variable models by attractor neural networks is studied. Memories are stored in a dynamical attractor that is a continuous manifold of fixed points, as illustrated by linear and nonlinear networks with hidden neurons. Pattern analysis and synthesis are forms of pattern completion by recall of a stored memory. Analysis and synthesis in the linear network are performed by bottom-up and top-down connections. In the nonlinear network, the analysis computation additionally requires rectification nonlinearity and inner product inhibition between hidden neurons. One popular approach to sensory processing is based on generative models, which assume that sensory input patterns are synthesized from some underlying hidden variables. For example, the sounds of speech can be synthesized from a sequence of phonemes, and images of a face can be synthesized from pose and lighting variables. Hidden variables are useful because they constitute a simpler representation of the variables that are visible in the sensory input. Using a generative model for sensory processing requires a method of pattern analysis. Given a sensory input pattern, analysis is the recovery of the hidden variables from which it was synthesized. In other words, analysis and synthesis are inverses of each other. There are a number of approaches to pattern analysis. In analysis-by-synthesis, the synthetic model is embedded inside a negative feedback loop[1]. Another approach is to construct a separate analysis model[2]. This paper explores a third approach, in which visible-hidden pairs are embedded as attractive fixed points, or attractors, in the state space of a recurrent neural network. The attractors can be regarded as memories stored in the network, and analysis and synthesis as forms of pattern completion by recall of a memory. The approach is illustrated with linear and nonlinear network architectures. In both networks, the synthetic model is linear, as in principal Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66986. 	[Title] Learning Continuous Attractors in Recurrent Networks [Abstract] One approach to invariant object recognition employs a recurrent neural network as an associative memory. In the standard depiction of the network's state space, memories of objects are stored as attractive fixed points of the dynamics. I argue for a modification of this picture: if an object has a continuous family of instantiations, it should be represented by a continuous attractor. This idea is illustrated with a network that learns to complete patterns. To perform the task of filling in missing information, the network develops a continuous attractor that models the manifold from which the patterns are drawn. From a statistical viewpoint, the pattern completion task allows a formulation of unsupervised A classic approach to invariant object recognition is to use a recurrent neural network as an associative memory[1]. In spite of the intuitive appeal and biological plausibility of this approach, it has largely been abandoned in practical applications. This paper introduces two new concepts that could help resurrect it: object representation by continuous attractors, and learning attractors by pattern completion. In most models of associative memory, memories are stored as attractive fixed points at discrete locations in state space[1]. Discrete attractors may not be appropriate for patterns with continuous variability, like the images of a three-dimensional object from different viewpoints. When the instantiations of an object lie on a continuous pattern manifold, it is more appropriate to represent objects by attractive manifolds of fixed points, or continuous attractors. To make this idea practical, it is important to find methods for learning attractors from examples. A naive method is to train the network to retain examples in short-term memory. This method is deficient because it does not prevent the network from storing spurious fixed points that are unrelated to the examples. A superior method is to train the network to restore examples that have been corrupted, so that it learns to complete patterns by filling in missing information. learning in terms of regression rather than density estimation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66990. 	[Title] Generative Models for Discovering Sparse Distributed Representations [Abstract] We describe a hierarchical, generative model that can be viewed as a non-linear generalization of factor analysis and can be implemented in a neural network. The model uses bottom-up, top-down and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demon strate that the network learns to extract sparse, distributed, hierarchical representations. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #194223. 	[Title] Bayesian Unsupervised Learning of Higher Order Structure [Abstract] Multilayer architectures such as those used in Bayesian belief networks and Helmholtz machines provide a powerful framework for representing and learning higher order statistical relations among inputs. Because exact probability calculations with these models are often intractable, there is much interest in finding approximate algorithms. We present an algorithm that efficiently discovers higher order structure using EM and Gibbs sampling. The model can be interpreted as a stochastic recurrent network in which ambiguity in lower-level states is resolved through feedback from higher levels. We demonstrate the performance of the algorithm on bench mark problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1140547. 	[Title] Localist Attractor Networks [Abstract] Attractor networks, which map a continuous input space to a discrete output space, are useful for pattern completion, cleaning up noisy or missing features in an input. However, designing a net to have a given set of attractors is notoriously tricky; training procedures are CPU intensive and often produce spurious attractors and ill-conditioned attractor basins. These difficulties occur because each connection in the network participates in the encoding of multiple attractors. We describe an alternative formulation of attractor networks in which the encoding of knowledge is local, not distributed. Although localist attractor nets have similar dynamics to their distributed counterparts, they are much easier to work with and interpret. We propose a statistical formulation of localist attractor net dynamics, which yields a convergence proof and a mathematical interpretation of model parameters. We present simulation experiments that explore the behavior of lo-calist attractor nets, showing that they produce a gang effectthe presence of an attractor enhances the attractor basins of neighboring attractorsand that spurious attractors occur only at points of symmetry in state space. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35922. 	[Title] Mean Field Theory for Sigmoid Belief Networks [Abstract] We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition|the classification of handwritten digits. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #11093. 	[Title] Factorial Learning and the EM Algorithm [Abstract] Many real world learning problems are best characterized by an interaction of multiple independent causes or factors. Discovering such causal structure from the data is the focus of this paper. Based on Zemel and Hinton's cooperative vector quantizer (CVQ) architecture, an unsupervised learning algorithm is derived from the Expectation-Maximization (EM) framework. Due to the combinatorial nature of the data generation process, the exact E-step is computationally intractable. Two alternative methods for computing the E-step are proposed: Gibbs sampling and mean-field approximation, and some promising empirical results are presented. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105116. 	[Title] Large Deviation Methods for Approximate Probabilistic Inference, with Rates of Convergence a free parameter. The [Abstract] We study layered belief networks of binary random variables in which the conditional probabilities Pr[childjparents] depend monotonically on weighted sums of the parents. For these networks, we give efficient algorithms for computing rigorous bounds on the marginal probabilities of evidence at the output layer. Our methods apply generally to the computation of both upper and lower bounds, as well as to generic transfer function parameterizations of the conditional probability tables (such as sigmoid and noisy-OR). We also prove rates of convergence of the accuracy of our bounds as a function of network size. Our results are derived by applying the theory of large deviations to the weighted sums of parents at each node in the network. Bounds on the marginal probabilities are computed from two contributions: one assuming that these weighted sums fall near their mean values, and the other assuming that they do not. This gives rise to an interesting trade-off between probable explanations of the evidence and improbable deviations from the mean. In networks where each child has N parents, the gap between our upper and lower bounds behaves as a sum of two terms, one of order p In addition to providing such rates of convergence for large networks, our methods also yield efficient algorithms for approximate inference in fixed networks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #390894. 	[Title] A variational approach to Bayesian logistic regression models and their extensions [Abstract] We consider a logistic regression model with a Gaussian prior distribution over the parameters. We show that accurate variational techniques can be used to obtain a closed form posterior distribution over the parameters given the data thereby yielding a posterior predictive model. The results are readily extended to (binary) belief networks. For belief networks we also derive closed form posteriors in the presence of missing values. Finally, we show that the dual of the regression problem gives a latent variable density model, the variational formulation of which leads to exactly solvable EM updates. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4335. 	[Title] A VIEW OF THE EM ALGORITHM THAT JUSTIFIES INCREMENTAL, SPARSE, AND OTHER VARIANTS [Abstract] The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #390896. 	[Title] IMPROVING THE MEAN FIELD APPROXIMATION VIA THE USE OF MIXTURE DISTRIBUTIONS [Abstract] Mean field methods provide computationally efficient approximations to posterior probability distributions for graphical models. Simple mean field methods make a completely factorized approximation to the posterior, which is unlikely to be accurate when the posterior is multimodal. Indeed, if the posterior is multi-modal, only one of the modes can be captured. To improve the mean field approximation in such cases, we employ mixture models as posterior approximations, where each mixture component is a factorized distribution. We describe efficient methods for optimizing the parameters in these models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #396412. 	[Title] Boltzmann Machine learning using mean field theory and linear response correction [Abstract] We present a new approximate learning algorithm for Boltzmann Machines, using a systematic expansion of the Gibbs free energy to second order in the weights. The linear response correction to the correlations is given by the Hessian of the Gibbs free energy. The computational complexity of the algorithm is cubic in the number of neurons. We compare the performance of the exact BM learning algorithm with first order (Weiss) mean field theory and second order (TAP) mean field theory. The learning task consists of a fully connected Ising spin glass model on 10 neurons. We conclude that 1) the method works well for paramagnetic problems 2) the TAP correction gives a significant improvement over the Weiss mean field theory, both for paramagnetic and spin glass problems and 3) that the inclusion of diagonal weights improves the Weiss approximation for paramagnetic problems, but not for spin glass problems. Please summarise all the given information.

Paper #66982 has the title `Learning Generative Models with the Up-Propagation Algorithm  
` and the abstract `Up-propagation is an algorithm for inverting and learning neural network generative models. Sensory input is processed by inverting a model that generates patterns from hidden variables using top-down connections. The inversion process is iterative, utilizing a negative feedback loop that depends on an error signal propagated by bottom-up connections. The error signal is also used to learn the generative model from examples. The algorithm is benchmarked against principal component analysis in In his doctrine of unconscious inference, Helmholtz argued that perceptions are formed by the interaction of bottom-up sensory data with top-down expectations. According to one interpretation of this doctrine, perception is a procedure of sequential hypothesis testing. We propose a new algorithm, called up-propagation, that realizes this interpretation in layered neural networks. It uses top-down connections to generate hypotheses, and bottom-up connections to revise them. It is important to understand the difference between up-propagation and its ancestor, the backpropagation algorithm[1]. Backpropagation is a learning algorithm for recognition models. As shown in Figure 1a, bottom-up connections recognize patterns, while top-down connections propagate an error signal that is used to learn the recognition model. In contrast, up-propagation is an algorithm for inverting and learning generative models, as shown in Figure 1b. Top-down connections generate patterns from a set of hidden variables. Sensory input is processed by inverting the generative model, recovering hidden variables that could have generated the sensory data. This operation is called either pattern recognition or pattern analysis, depending on the meaning of the hidden variables. Inversion of the generative model is done iteratively, through a negative feedback loop driven by an error signal from the bottom-up connections. The error signal is also used for learning the connections experiments on images of handwritten digits.
`.
Question: Which category should Paper #66982 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #66982 has the title `Learning Generative Models with the Up-Propagation Algorithm  
` and the abstract `Up-propagation is an algorithm for inverting and learning neural network generative models. Sensory input is processed by inverting a model that generates patterns from hidden variables using top-down connections. The inversion process is iterative, utilizing a negative feedback loop that depends on an error signal propagated by bottom-up connections. The error signal is also used to learn the generative model from examples. The algorithm is benchmarked against principal component analysis in In his doctrine of unconscious inference, Helmholtz argued that perceptions are formed by the interaction of bottom-up sensory data with top-down expectations. According to one interpretation of this doctrine, perception is a procedure of sequential hypothesis testing. We propose a new algorithm, called up-propagation, that realizes this interpretation in layered neural networks. It uses top-down connections to generate hypotheses, and bottom-up connections to revise them. It is important to understand the difference between up-propagation and its ancestor, the backpropagation algorithm[1]. Backpropagation is a learning algorithm for recognition models. As shown in Figure 1a, bottom-up connections recognize patterns, while top-down connections propagate an error signal that is used to learn the recognition model. In contrast, up-propagation is an algorithm for inverting and learning generative models, as shown in Figure 1b. Top-down connections generate patterns from a set of hidden variables. Sensory input is processed by inverting the generative model, recovering hidden variables that could have generated the sensory data. This operation is called either pattern recognition or pattern analysis, depending on the meaning of the hidden variables. Inversion of the generative model is done iteratively, through a negative feedback loop driven by an error signal from the bottom-up connections. The error signal is also used for learning the connections experiments on images of handwritten digits.
`.
Question: Which category should Paper #66982 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks