Above are papers related to the following paper: [Paper_ID] Paper #91038. 	[Title] Learning Stochastic Feedforward Networks [Abstract] Connectionist learning procedures are presented for "sigmoid" and "noisy-OR" varieties of stochastic feedforward network. These networks are in the same class as the "belief networks" used in expert systems. They represent a probability distribution over a set of visible variables using hidden variables to express correlations. Conditional probability distributions can be exhibited by stochastic simulation for use in tasks such as classification. Learning from empirical data is done via a gradient-ascent method analogous to that used in Boltzmann machines, but due to the feedforward nature of the connections, the negative phase of Boltzmann machine learning is unnecessary. Experimental results show that, as a result, learning in a sigmoid feedforward network can be faster than in a Boltzmann machine. These networks have other advantages over Boltzmann machines in pattern classification and decision making applications, and provide a link between work on connectionist learning and work on the representation of expert knowledge. 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 #300806. 	[Title] Learning in Boltzmann Trees [Abstract] We introduce a large family of Boltzmann machines that can be trained using standard gradient descent. The networks can have one or more layers of hidden units, with tree-like connectivity. We show how to implement the supervised learning algorithm for these Boltzmann machines exactly, without resort to simulated or mean-field annealing. The stochastic averages that yield the gradients in weight space are computed by the technique of decimation. We present results on the problems of N -bit parity and the detection of hidden symmetries. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #446271. 	[Title] Mapping Bayesian Networks to Boltzmann Machines [Abstract] We study the task of tnding a maximal a posteriori (MAP) instantiation of Bayesian network variables, given a partial value assignment as an initial constraint. This problem is known to be NP-hard, so we concentrate on a stochastic approximation algorithm, simulated annealing. This stochastic algorithm can be realized as a sequential process on the set of Bayesian network variables, where only one variable is allowed to change at a time. Consequently, the method can become impractically slow as the number of variables increases. We present a method for mapping a given Bayesian network to a massively parallel Bolztmann machine neural network architecture, in the sense that instead of using the normal sequential simulated annealing algorithm, we can use a massively parallel stochastic process on the Boltzmann machine architecture. The neural network updating process provably converges to a state which solves a given MAP task. 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.

Paper #91038 has the title `Learning Stochastic Feedforward Networks  
` and the abstract `Connectionist learning procedures are presented for "sigmoid" and "noisy-OR" varieties of stochastic feedforward network. These networks are in the same class as the "belief networks" used in expert systems. They represent a probability distribution over a set of visible variables using hidden variables to express correlations. Conditional probability distributions can be exhibited by stochastic simulation for use in tasks such as classification. Learning from empirical data is done via a gradient-ascent method analogous to that used in Boltzmann machines, but due to the feedforward nature of the connections, the negative phase of Boltzmann machine learning is unnecessary. Experimental results show that, as a result, learning in a sigmoid feedforward network can be faster than in a Boltzmann machine. These networks have other advantages over Boltzmann machines in pattern classification and decision making applications, and provide a link between work on connectionist learning and work on the representation of expert knowledge. 
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Question: Which category should Paper #91038 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #91038 has the title `Learning Stochastic Feedforward Networks  
` and the abstract `Connectionist learning procedures are presented for "sigmoid" and "noisy-OR" varieties of stochastic feedforward network. These networks are in the same class as the "belief networks" used in expert systems. They represent a probability distribution over a set of visible variables using hidden variables to express correlations. Conditional probability distributions can be exhibited by stochastic simulation for use in tasks such as classification. Learning from empirical data is done via a gradient-ascent method analogous to that used in Boltzmann machines, but due to the feedforward nature of the connections, the negative phase of Boltzmann machine learning is unnecessary. Experimental results show that, as a result, learning in a sigmoid feedforward network can be faster than in a Boltzmann machine. These networks have other advantages over Boltzmann machines in pattern classification and decision making applications, and provide a link between work on connectionist learning and work on the representation of expert knowledge. 
`.
Question: Which category should Paper #91038 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: Probabilistic_Methods