Above are papers related to the following paper: [Paper_ID] Paper #202520. 	[Title] Using Bayesian networks for incorporating probabilistic a priori knowledge into Boltzmann machines [Abstract] We present a method for automatically determining the structure and the connection weights of a Boltzmann machine corresponding to a given Bayesian network representation of a probability distribution on a set of discrete variables. The resulting Boltzmann machine structure can be implemented efficiently on massively parallel hardware, since the structure can be divided into two separate clusters where all the nodes in one cluster can be updated simultaneously. The updating process of the Boltzmann machine approximates a Gibbs sampling process of the original Bayesian network in the sense that the Boltzmann machine converges to the same final state as the Gibbs sampler does. The mapping from a Bayesian network to a Boltzmann machine can be seen as a method for incorporating probabilistic a priori information into a neural network architecture, which can then be trained further with existing learning algorithms. 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 #1115701. 	[Title] Learning Bayesian Prototype Trees by Simulated Annealing [Abstract] Given a set of samples of an unknown probability distribution, we study the problem of constructing a good approximative Bayesian network model of the probability distribution in question. This task can be viewed as a search problem, where the goal is to find a maximal probability network model, given the data. In this work, we do not make an attempt to learn arbitrarily complex multi-connected Bayesian network structures, since such resulting models can be unsuitable for practical purposes due to the exponential amount of time required for the reasoning task. Instead, we restrict ourselves to a special class of simple tree-structured Bayesian networks called Bayesian prototype trees, for which a polynomial time algorithm for Bayesian reasoning exists. We show how the probability of a given Bayesian prototype tree model can be evaluated, given the data, and how this evaluation criterion can be used in a stochastic simulated annealing algorithm for searching the model space. The simulated annealing algorithm provably finds the maximal probability model, provided that a sufficient amount of time is used. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #31479. 	[Title] Induction of Selective Bayesian Classifiers [Abstract] In this paper, we examine previous work on the naive Bayesian classifier and review its limitations, which include a sensitivity to correlated features. We respond to this problem by embedding the naive Bayesian induction scheme within an algorithm that carries out a greedy search through the space of features. We hypothesize that this approach will improve asymptotic accuracy in domains that involve correlated features without reducing the rate of learning in ones that do not. We report experimental results on six natural domains, including comparisons with decision-tree induction, that support these hypotheses. In closing, we discuss other approaches to extending naive Bayesian classifiers and outline some directions for future research. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #202522. 	[Title] Constructing Computationally Efficient Bayesian Models via Unsupervised Clustering  Probabilistic Reasoning and Bayesian Belief Networks, [Abstract] Given a set of samples of an unknown probability distribution, we study the problem of constructing a good approximative Bayesian network model of the probability distribution in question. This task can be viewed as a search problem, where the goal is to find a maximal probability network model, given the data. In this work, we do not make an attempt to learn arbitrarily complex multi-connected Bayesian network structures, since such resulting models can be unsuitable for practical purposes due to the exponential amount of time required for the reasoning task. Instead, we restrict ourselves to a special class of simple tree-structured Bayesian networks called Bayesian prototype trees, for which a polynomial time algorithm for Bayesian reasoning exists. We show how the probability of a given Bayesian prototype tree model can be evaluated, given the data, and how this evaluation criterion can be used in a stochastic simulated annealing algorithm for searching the model space. The simulated annealing algorithm provably finds the maximal probability model, provided that a sufficient amount of time is used. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20923. 	[Title] Bayesian Case-Based Reasoning with Neural Networks [Abstract] Given a problem, a case-based reasoning (CBR) system will search its case memory and use the stored cases to find the solution, possibly modifying retrieved cases to adapt to the required input specifications. In this paper we introduce a neural network architecture for efficient case-based reasoning. We show how a rigorous Bayesian probability propagation algorithm can be implemented as a feedforward neural network and adapted for CBR. In our approach the efficient indexing problem of CBR is naturally implemented by the parallel architecture, and heuristic matching is replaced by a probability metric. This allows our CBR to perform theoretically sound Bayesian reasoning. We also show how the probability propagation actually offers a solution to the adaptation problem in a very natural way. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20924. 	[Title] Massively Parallel Case-Based Reasoning with Probabilistic Similarity Metrics [Abstract] We propose a probabilistic case-space metric for the case matching and case adaptation tasks. Central to our approach is a probability propagation algorithm adopted from Bayesian reasoning systems, which allows our case-based reasoning system to perform theoretically sound probabilistic reasoning. The same probability propagation mechanism actually offers a uniform solution to both the case matching and case adaptation problems. We also show how the algorithm can be implemented as a connectionist network, where efficient massively parallel case retrieval is an inherent property of the system. We argue that using this kind of an approach, the difficult problem of case indexing can be completely avoided. Pp. 144-154 in Topics in Case-Based Reasoning, edited by Stefan Wess, Klaus-Dieter Althoff and Michael M. Richter. Volume 837, Lecture Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #289885. 	[Title] Learning in neural networks with Bayesian prototypes [Abstract] Given a set of samples of a probability distribution on a set of discrete random variables, we study the problem of constructing a good approximative neural network model of the underlying probability distribution. Our approach is based on an unsupervised learning scheme where the samples are first divided into separate clusters, and each cluster is then coded as a single vector. These Bayesian prototype vectors consist of conditional probabilities representing the attribute-value distribution inside the corresponding cluster. Using these prototype vectors, it is possible to model the underlying joint probability distribution as a simple Bayesian network (a tree), which can be realized as a feedforward neural network capable of probabilistic reasoning. In this framework, learning means choosing the size of the prototype set, partitioning the samples into the corresponding clusters, and constructing the cluster prototypes. We describe how the prototypes can be determined, given a partition of the samples, and present a method for evaluating the likelihood of the corresponding Bayesian tree. We also present a greedy heuristic for searching through the space of different partition schemes with different numbers of clusters, aiming at an optimal approximation of the probability distribution. 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.

Paper #202520 has the title `Using Bayesian networks for incorporating probabilistic a priori knowledge into Boltzmann machines  
` and the abstract `We present a method for automatically determining the structure and the connection weights of a Boltzmann machine corresponding to a given Bayesian network representation of a probability distribution on a set of discrete variables. The resulting Boltzmann machine structure can be implemented efficiently on massively parallel hardware, since the structure can be divided into two separate clusters where all the nodes in one cluster can be updated simultaneously. The updating process of the Boltzmann machine approximates a Gibbs sampling process of the original Bayesian network in the sense that the Boltzmann machine converges to the same final state as the Gibbs sampler does. The mapping from a Bayesian network to a Boltzmann machine can be seen as a method for incorporating probabilistic a priori information into a neural network architecture, which can then be trained further with existing learning algorithms. 
`.
Question: Which category should Paper #202520 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #202520 has the title `Using Bayesian networks for incorporating probabilistic a priori knowledge into Boltzmann machines  
` and the abstract `We present a method for automatically determining the structure and the connection weights of a Boltzmann machine corresponding to a given Bayesian network representation of a probability distribution on a set of discrete variables. The resulting Boltzmann machine structure can be implemented efficiently on massively parallel hardware, since the structure can be divided into two separate clusters where all the nodes in one cluster can be updated simultaneously. The updating process of the Boltzmann machine approximates a Gibbs sampling process of the original Bayesian network in the sense that the Boltzmann machine converges to the same final state as the Gibbs sampler does. The mapping from a Bayesian network to a Boltzmann machine can be seen as a method for incorporating probabilistic a priori information into a neural network architecture, which can then be trained further with existing learning algorithms. 
`.
Question: Which category should Paper #202520 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