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 #1108267. 	[Title] Cooperative Bayesian and Case-Based Reasoning for Solving Multiagent Planning Tasks [Abstract] We describe an integrated problem solving architecture named INBANCA in which Bayesian networks and case-based reasoning (CBR) work cooperatively on multiagent planning tasks. This includes two-team dynamic tasks, and this paper concentrates on simulated soccer as an example. Bayesian networks are used to characterize action selection whereas a case-based approach is used to determine how to implement actions. This paper has two contributions. First, we survey integrations of case-based and Bayesian approaches from the perspective of a popular CBR task decomposition framework, thus explaining what types of integrations have been attempted. This allows us to explain the unique aspects of our proposed integration. Second, we demonstrate how Bayesian nets can be used to provide environmental context, and thus feature selection information, for the case-based reasoner. 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 #114189. 	[Title] Searching for dependencies in Bayesian classifiers j A n V n j If the attributes [Abstract] Naive Bayesian classifiers which make independence assumptions perform remarkably well on some data sets but poorly on others. We explore ways to improve the Bayesian classifier by searching for dependencies among attributes. We propose and evaluate two algorithms for detecting dependencies among attributes and show that the backward sequential elimination and joining algorithm provides the most improvement over the naive Bayesian classifier. The domains on which the most improvement occurs are those domains on which the naive Bayesian classifier is significantly less accurate than a decision tree learner. This suggests that the attributes used in some common databases are not independent conditioned on the class and that the violations of the independence assumption that affect the accuracy of the classifier The Bayesian classifier (Duda & Hart, 1973) is a probabilistic method for classification. It can be used to determine the probability that an example j belongs to class C i given values of attributes of an example represented as a set of n nominally-valued attribute-value pairs of the form A 1 = V 1 j : ^ P (A k = V k j jC i ) may be estimated from the training data. To determine the most likely class of a test example, the probability of each class is computed with Equation 1. A classifier created in this manner is sometimes called a simple (Langley, 1993) or naive (Kononenko, 1990) Bayesian classifier. One important evaluation metric for machine learning methods is the predictive accuracy on unseen examples. This is measured by randomly selecting a subset of the examples in a database to use as training examples and reserving the remainder to be used as test examples. In the case of the simple Bayesian classifier, the training examples are used to estimate probabilities and Equation 1.1 is then used can be detected from training data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1113934. 	[Title] Integration of Case-Based Reasoning and Neural Networks Approaches for Classification [Abstract] Several different approaches have been used to describe concepts for supervised learning tasks. In this paper we describe two approaches which are: prototype-based incremental neural networks and case-based reasoning approaches. We show then how we can improve a prototype-based neural network model by storing some specific instances in a CBR memory system. This leads us to propose a co-processing hybrid model for classification. 1 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #294030. 	[Title] MDL Learning of Probabilistic Neural Networks for Discrete Problem Domains [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 discrete domains CBR reasoning can be based on a rigorous Bayesian probability propagation algorithm. Such a Bayesian CBR system can be implemented as a probabilistic feedforward neural network with one of the layers representing the cases. In this paper we introduce a Minimum Description Length (MDL) based learning algorithm to obtain the proper network structure with the associated conditional probabilities. This algorithm together with the resulting neural network implementation provide a massively parallel architecture for solving the efficiency bottleneck in case-based reasoning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20592. 	[Title] Learning NonLinearly Separable Boolean Functions With Linear Threshold Unit Trees and Madaline-Style Networks [Abstract] This paper investigates an algorithm for the construction of decisions trees comprised of linear threshold units and also presents a novel algorithm for the learning of non-linearly separable boolean functions using Madaline-style networks which are isomorphic to decision trees. The construction of such networks is discussed, and their performance in learning is compared with standard BackPropagation on a sample problem in which many irrelevant attributes are introduced. Littlestone's Winnow algorithm is also explored within this architecture as a means of learning in the presence of many irrelevant attributes. The learning ability of this Madaline-style architecture on nonoptimal (larger than necessary) networks is also explored. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1116530. 	[Title] NEULA: A hybrid neural-symbolic expert system shell [Abstract] Current expert systems cannot properly handle imprecise and incomplete information. On the other hand, neural networks can perform pattern recognition operations even in noisy environments. Against this background, we have implemented a neural expert system shell NEULA, whose computational mechanism processes imprecisely or incompletely given information by means of approximate probabilistic reasoning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #14549. 	[Title] Recognition and Exploitation of Contextual Clues via Incremental Meta-Learning (Extended Version) [Abstract] Daily experience shows that in the real world, the meaning of many concepts heavily depends on some implicit context, and changes in that context can cause more or less radical changes in the concepts. Incremental concept learning in such domains requires the ability to recognize and adapt to such changes. This paper presents a solution for incremental learning tasks where the domain provides explicit clues as to the current context (e.g., attributes with characteristic values). We present a general two-level learning model, and its realization in a system named MetaL(B), that can learn to detect certain types of contextual clues, and can react accordingly when a context change is suspected. The model consists of a base level learner that performs the regular on-line learning and classification task, and a meta-learner that identifies potential contextual clues. Context learning and detection occur during regular on-line learning, without separate training phases for context recognition. Experiments with synthetic domains as well as a `real-world' problem show that MetaL(B) is robust in a variety of dimensions and produces substantial improvement over simple object-level learning in situations with changing contexts. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #521207. 	[Title] A Formal Analysis of Case Base Retrieval [Abstract] Case based systems typically retrieve cases from the case base by applying similarity measures. The measures are usually constructed in an ad hoc manner. This report presents a toolbox for the systematic construction of similarity measures. In addition to paving the way to a design methodology for similarity measures, this systematic approach facilitates the identification of opportunities for parallelisation in case base retrieval. Please summarise all the given information.

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 #39165. 	[Title] Efficient Learning of Selective Bayesian Network Classifiers [Abstract] In this paper, we present a computation-ally efficient method for inducing selective Bayesian network classifiers. Our approach is to use information-theoretic metrics to efficiently select a subset of attributes from which to learn the classifier. We explore three conditional, information-theoretic met-rics that are extensions of metrics used extensively in decision tree learning, namely Quin-lan's gain and gain ratio metrics and Man-taras's distance metric. We experimentally show that the algorithms based on gain ratio and distance metric learn selective Bayesian networks that have predictive accuracies as good as or better than those learned by existing selective Bayesian network induction approaches (K2-AS), but at a significantly lower computational cost. We prove that the subset-selection phase of these information-based algorithms has polynomial complexity, as compared to the worst-case exponential time complexity of the corresponding phase in K2-AS. 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 #77758. 	[Title] Parzen. On estimation of a probability density function and mode. Annual Mathematical Statistics, 33:1065-1076, 1962. [Abstract] To apply the algorithm for classification we assign each class a separate set of codebook Gaussians. Each set is only trained with patterns from a single class. After having trained the codebook Gaussians, each set provides an estimate of the probability function of one class; just as with Parzen window estimation, we take as the estimate of the pattern distribution the average of all Gaussians in the set. Classification of a pattern may now be done by calculating the probability of each class at the respective sample point, and assigning to the pattern the class with the highest probability. Hence the whole codebook plays a role in the classification of patterns. This is not the case with regular classification schemes using codebooks. We have tested the classification scheme on several classification tasks including the two spiral problem. We compared our algorithm to various other classification algorithms and it came out second; the best algorithm for the applications is the Parzen window estimation. However, the computing time and memory for Parzen window estimation are excessive when compared to our algorithm, and hence, in practical situations, our algorithm is to be preferred. We have developed a fast algorithm which combines attractive properties of both Parzen window estimation and vector quantization. The scale parameter is tuned adaptively and, therefore, is not set in an ad hoc manner. It allows a classification strategy in which all the codebook vectors are taken into account. This yields better results than the standard vector quantization techniques. An interesting topic for further research is to use radially non-symmetric Gaussians. 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 #1115701 has the title `Learning Bayesian Prototype Trees by Simulated Annealing  
` and the 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. 
`.
Question: Which category should Paper #1115701 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1115701 has the title `Learning Bayesian Prototype Trees by Simulated Annealing  
` and the 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. 
`.
Question: Which category should Paper #1115701 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