Above are papers related to the following paper: [Paper_ID] Paper #3222. 	[Title] Beyond Independence: Conditions for the Optimality of the Simple Bayesian Classifier [Abstract] The simple Bayesian classifier (SBC) is commonly thought to assume that attributes are independent given the class, but this is apparently contradicted by the surprisingly good performance it exhibits in many domains that contain clear attribute dependences. No explanation for this has been proposed so far. In this paper we show that the SBC does not in fact assume attribute independence, and can be optimal even when this assumption is violated by a wide margin. The key to this finding lies in the distinction between classification and probability estimation: correct classification can be achieved even when the probability estimates used contain large errors. We show that the previously-assumed region of optimality of the SBC is a second-order infinitesimal fraction of the actual one. This is followed by the derivation of several necessary and several sufficient conditions for the optimality of the SBC. For example, the SBC is optimal for learning arbitrary conjunctions and disjunctions, even though they violate the independence assumption. The paper also reports empirical evidence of the SBC's competitive performance in domains containing substantial degrees of attribute dependence. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131137. 	[Title] Mining and Model Simplicity: A Case Study in Diagnosis [Abstract] Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD), 1996. The official version of this paper has been published by the American Association for Artificial Intelligence (http://www.aaai.org) c fl 1996, American Association for Artificial Intelligence. All rights reserved. Abstract We describe the results of performing data mining on a challenging medical diagnosis domain, acute abdominal pain. This domain is well known to be difficult, yielding little more than 60% predictive accuracy for most human and machine diagnosticians. Moreover, many researchers argue that one of the simplest approaches, the naive Bayesian classifier, is optimal. By comparing the performance of the naive Bayesian classifier to its more general cousin, the Bayesian network classifier, and to selective Bayesian classifiers with just 10% of the total attributes, we show that the simplest models perform at least as well as the more complex models. We argue that simple models like the selective naive Bayesian classifier will perform as well as more complicated models for similarly complex domains with relatively small data sets, thereby calling into question the extra expense necessary to induce more complex models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #8079. 	[Title] Bias Plus Variance Decomposition for Zero-One Loss Functions [Abstract] We present a bias-variance decomposition of expected misclassification rate, the most commonly used loss function in supervised classification learning. The bias-variance decomposition for quadratic loss functions is well known and serves as an important tool for analyzing learning algorithms, yet no decomposition was offered for the more commonly used zero-one (misclassification) loss functions until the recent work of Kong & Dietterich (1995) and Breiman (1996). Their decomposition suffers from some major shortcomings though (e.g., potentially negative variance), which our decomposition avoids. We show that, in practice, the naive frequency-based estimation of the decomposition terms is by itself biased and show how to correct for this bias. We illustrate the decomposition on various algorithms and datasets from the UCI repository. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3223. 	[Title] Supervised and Unsupervised Discretization of Continuous Features [Abstract] Many supervised machine learning algorithms require a discrete feature space. In this paper, we review previous work on continuous feature discretization, identify defining characteristics of the methods, and conduct an empirical evaluation of several methods. We compare binning, an unsupervised discretization method, to entropy-based and purity-based methods, which are supervised algorithms. We found that the performance of the Naive-Bayes algorithm significantly improved when features were discretized using an entropy-based method. In fact, over the 16 tested datasets, the discretized version of Naive-Bayes slightly outperformed C4.5 on average. We also show that in some cases, the performance of the C4.5 induction algorithm significantly improved if features were discretized in advance; in our experiments, the performance never significantly degraded, an interesting phenomenon considering the fact that C4.5 is capable of locally discretiz ing features. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #964248. 	[Title] Issues in the Integration of Data Mining and Data Visualization Visualizing the Simple Bayesian Classifier [Abstract] The simple Bayesian classifier (SBC), sometimes called Naive-Bayes, is built based on a conditional independence model of each attribute given the class. The model was previously shown to be surprisingly robust to obvious violations of this independence assumption, yielding accurate classification models even when there are clear conditional dependencies. The SBC can serve as an excellent tool for initial exploratory data analysis when coupled with a visualizer that makes its structure comprehensible. We describe such a visual representation of the SBC model that has been successfully implemented. We describe the requirements we had for such a visualization and the design decisions we made to satisfy them. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3233. 	[Title] A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection [Abstract] We review accuracy estimation methods and compare the two most common methods: cross-validation and bootstrap. Recent experimental results on artificial data and theoretical results in restricted settings have shown that for selecting a good classifier from a set of classifiers (model selection), ten-fold cross-validation may be better than the more expensive leave-one-out cross-validation. We report on a large-scale experiment|over half a million runs of C4.5 and a Naive-Bayes algorithm|to estimate the effects of different parameters on these algorithms on real-world datasets. For cross-validation, we vary the number of folds and whether the folds are stratified or not; for bootstrap, we vary the number of bootstrap samples. Our results indicate that for real-word datasets similar to ours, the best method to use for model selection is ten-fold stratified cross validation, even if computation power allows using more folds. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3235. 	[Title] Scaling Up the Accuracy of Naive-Bayes Classifiers: a Decision-Tree Hybrid [Abstract] Naive-Bayes induction algorithms were previously shown to be surprisingly accurate on many classification tasks even when the conditional independence assumption on which they are based is violated. However, most studies were done on small databases. We show that in some larger databases, the accuracy of Naive-Bayes does not scale up as well as decision trees. We then propose a new algorithm, NBTree, which induces a hybrid of decision-tree classifiers and Naive-Bayes classifiers: the decision-tree nodes contain uni-variate splits as regular decision-trees, but the leaves contain Naive-Bayesian classifiers. The approach retains the interpretability of Naive-Bayes and decision trees, while resulting in classifiers that frequently outperform both constituents, especially in the larger databases tested. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3237. 	[Title] Feature Subset Selection Using the Wrapper Method: Overfitting and Dynamic Search Space Topology [Abstract] In the wrapper approach to feature subset selection, a search for an optimal set of features is made using the induction algorithm as a black box. The estimated future performance of the algorithm is the heuristic guiding the search. Statistical methods for feature subset selection including forward selection, backward elimination, and their stepwise variants can be viewed as simple hill-climbing techniques in the space of feature subsets. We utilize best-first search to find a good feature subset and discuss overfitting problems that may be associated with searching too many feature subsets. We introduce compound operators that dynamically change the topology of the search space to better utilize the information available from the evaluation of feature subsets. We show that compound operators unify previous approaches that deal with relevant and irrelevant features. The improved feature subset selection yields significant improvements for real-world datasets when using the ID3 and the Naive-Bayes induction algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1132157. 	[Title] NAIVE BAYESIAN LEARNING  Adapted from [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3240. 	[Title] An Analysis of Bayesian Classifiers (1988), involves the formulation of average-case models for specific algorithms [Abstract] In this paper we present an average-case analysis of the Bayesian classifier, a simple induction algorithm that fares remarkably well on many learning tasks. Our analysis assumes a monotone conjunctive target concept, and independent, noise-free Boolean attributes. We calculate the probability that the algorithm will induce an arbitrary pair of concept descriptions and then use this to compute the probability of correct classification over the instance space. The analysis takes into account the number of training instances, the number of attributes, the distribution of these attributes, and the level of class noise. We also explore the behavioral implications of the analysis by presenting predicted learning curves for artificial domains, and give experimental results on these domains as a check on our reasoning. One goal of research in machine learning is to discover principles that relate algorithms and domain characteristics to behavior. To this end, many researchers have carried out systematic experimentation with natural and artificial domains in search of empirical regularities (e.g., Kibler & Langley, 1988). Others have focused on theoretical analyses, often within the paradigm of probably approximately correct learning (e.g., Haus-sler, 1990). However, most experimental studies are based only on informal analyses of the learning task, whereas most formal analyses address the worst case, and thus bear little relation to empirical results. ber of attributes, and the class and attribute frequencies, they obtain predictions about the behavior of induction algorithms and used experiments to check their analyses. 1 However, their research does not focus on algorithms typically used by the experimental and practical sides of machine learning, and it is important that average-case analyses be extended to such methods. Recently, there has been growing interest in probabilistic approaches to inductive learning. For example, Fisher (1987) has described Cobweb, an incremental algorithm for conceptual clustering that draws heavily on Bayesian ideas, and the literature reports a number of systems that build on this work (e.g., Allen & Lang-ley, 1990; Iba & Gennari, 1991; Thompson & Langley, 1991). Cheeseman et al. (1988) have outlined Auto-Class, a nonincremental system that uses Bayesian methods to cluster instances into groups, and other researchers have focused on the induction of Bayesian inference networks (e.g., Cooper & Kerskovits, 1991). These recent Bayesian learning algorithms are complex and not easily amenable to analysis, but they share a common ancestor that is simpler and more tractable. This supervised algorithm, which we refer to simply as a Bayesian classifier, comes originally from work in pattern recognition (Duda & Hart, 1973). The method stores a probabilistic summary for each class; this summary contains the conditional probability of each attribute value given the class, as well as the probability (or base rate) of the class. This data structure approximates the representational power of a perceptron; it describes a single decision boundary through the instance space. When the algorithm encounters a new instance, it updates the probabilities stored with the specified class. Neither the order of training instances nor the occurrence of classification errors have any effect on this process. When given a test instance, the classifier uses an evaluation function (which we describe in detail later) to rank the alter Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #92589. 	[Title] 28 Learning Bayesian Networks Using Feature Selection [Abstract] This paper introduces a novel enhancement for learning Bayesian networks with a bias for small, high-predictive-accuracy networks. The new approach selects a subset of features that maximizes predictive accuracy prior to the network learning phase. We examine explicitly the effects of two aspects of the algorithm, feature selection and node ordering. Our approach generates networks that are computationally simpler to evaluate and display predictive accuracy comparable Bayesian networks are being increasingly recognized as an important representation for probabilistic reasoning. For many domains, the need to specify the probability distributions for a Bayesian network is considerable, and learning these probabilities from data using an algorithm like K2 [Cooper92] could alleviate such specification difficulties. We describe an extension to the Bayesian network learning approaches introduced in K2. Our goal is to construct networks that are simpler to evaluate but still have high predictive accuracy relative to networks that model all features. Rather than use all database features (or attributes) for constructing the network, we select a subset of features that maximize the predictive accuracy of the network. Then the learning process uses only the selected features as nodes in learning the Bayesian network. We examine explicitly the effects of two aspects of the algorithm: (a) feature selection, and (b) node ordering. Our experimental results verify that this approach generates networks that are compu-tationally simpler to evaluate and display predictive accuracy comparable to the predictive accuracy of Bayesian networks that model all features. Our results, similar to those observed by other studies of feature selection in learning [Caruana94, John94, Langley94a, Langley94b], demonstrate that feature selection provides comparable predictive accuracy using smaller networks. For example, by selecting as few as 18% of the features for the to that of Bayesian networks which model all attributes. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5055. 	[Title] Boosting the Margin: A New Explanation for the Effectiveness of Voting Methods [Abstract] One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik's support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance decomposition. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18773. 	[Title] Building Classifiers using Bayesian Networks [Abstract] Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with state of the art classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we examine and evaluate approaches for inducing classifiers from data, based on recent results in the theory of learning Bayesian networks. Bayesian networks are factored representations of probability distributions that generalize the naive Bayes classifier and explicitly represent statements about independence. Among these approaches we single out a method we call Tree Augmented Naive Bayes (TAN), which outperforms naive Bayes, yet at the same time maintains the computational simplicity (no search involved) and robustness which are characteristic of naive Bayes. We experimentally tested these approaches using benchmark problems from the U. C. Irvine repository, and compared them against C4.5, naive Bayes, and wrapper-based feature selection methods. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #2653. 	[Title] A decision-theoretic generalization of on-line learning and an application to boosting how the weight-update rule [Abstract] We consider the problem of dynamically apportioning resources among a set of options in a worst-case on-line framework. The model we study can be interpreted as a broad, abstract extension of the well-studied on-line prediction model to a general decision-theoretic setting. We show that the multiplicative weight-update rule of Littlestone and Warmuth [10] can be adapted to this model yielding bounds that are slightly weaker in some cases, but applicable to a considerably more general class of learning problems. We show how the resulting learning algorithm can be applied to a variety of problems, including gambling, multiple-outcome prediction, repeated games and prediction of points in R n Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #167656. 	[Title] BOOSTING AND NAIVE BAYESIAN LEARNING [Abstract] Although so-called naive Bayesian classification makes the unrealistic assumption that the values of the attributes of an example are independent given the class of the example, this learning method is remarkably successful in practice, and no uniformly better learning method is known. Boosting is a general method of combining multiple classifiers due to Yoav Freund and Rob Schapire. This paper shows that boosting applied to naive Bayesian classifiers yields combination classifiers that are representationally equivalent to standard feedforward multilayer perceptrons. (An ancillary result is that naive Bayesian classification is a nonparametric, nonlinear generalization of logistic regression.) As a training algorithm, boosted naive Bayesian learning is quite different from backpropagation, and has definite advantages. Boosting requires only linear time and constant space, and hidden nodes are learned incrementally, starting with the most important. On the real-world datasets on which the method has been tried so far, generalization performance is as good as or better than the best published result using any other learning method. Unlike all other standard learning algorithms, naive Bayesian learning, with and without boosting, can be done in logarithmic time with a linear number of parallel computing units. Accordingly, these learning methods are highly plausible computationally as models of animal learning. Other arguments suggest that they are plausible behaviorally also. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4330. 	[Title] Hierarchical Mixtures of Experts and the EM Algorithm [Abstract] We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain. This report describes research done at the Dept. of Brain and Cognitive Sciences, the Center for Biological and Computational Learning, and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for CBCL is provided in part by a grant from the NSF (ASC-9217041). Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense. The authors were supported by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, by by grant IRI-9013991 from the National Science Foundation, by grant N00014-90-J-1942 from the Office of Naval Research, and by NSF grant ECS-9216531 to support an Initiative in Intelligent Control at MIT. Michael I. Jordan is a NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1114222. 	[Title] Lazy Bayesian Trees [Abstract] The naive Bayesian classifier is simple and effective, but its attribute independence assumption is often violated in the real world. A number of approaches have been developed that seek to alleviate this problem. A Bayesian tree learning algorithm builds a decision tree, and generates a local Bayesian classifier at each leaf instead of predicting a single class. However, Bayesian tree learning still suffers from the replication and fragmentation problems of tree learning. While inferred Bayesian trees demonstrate low average prediction error rates, there is reason to believe that error rates will be higher for those leaves with few training examples. This paper proposes a novel lazy Bayesian tree learning algorithm. For each test example, it conceptually builds a most appropriate Bayesian tree. In practice, only one path with a local Bayesian classifier at its leaf is created. Experiments with a wide variety of real-world and artificial domains show that this new algorithm has significantly lower overall prediction error rates than a naive Bayesian classifier, C4.5, and a Bayesian tree learning algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1103737. 	[Title] On learning hierarchical classifications [Abstract] Many significant real-world classification tasks involve a large number of categories which are arranged in a hierarchical structure; for example, classifying documents into subject categories under the library of congress scheme, or classifying world-wide-web documents into topic hierarchies. We investigate the potential benefits of using a given hierarchy over base classes to learn accurate multi-category classifiers for these domains. First, we consider the possibility of exploiting a class hierarchy as prior knowledge that can help one learn a more accurate classifier. We explore the benefits of learning category-discriminants in a hard top-down fashion and compare this to a soft approach which shares training data among sibling categories. In doing so, we verify that hierarchies have the potential to improve prediction accuracy. But we argue that the reasons for this can be subtle. Sometimes, the improvement is only because using a hierarchy happens to constrain the expressiveness of a hypothesis class in an appropriate manner. However, various controlled experiments show that in other cases the performance advantage associated with using a hierarchy really does seem to be due to the prior knowledge it encodes. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #31483. 	[Title] A Comparison of Induction Algorithms for Selective and non-Selective Bayesian Classifiers [Abstract] In this paper we present a novel induction algorithm for Bayesian networks. This selective Bayesian network classifier selects a subset of attributes that maximizes predictive accuracy prior to the network learning phase, thereby learning Bayesian networks with a bias for small, high-predictive-accuracy networks. We compare the performance of this classifier with selective and non-selective naive Bayesian classifiers. We show that the selective Bayesian network classifier performs significantly better than both versions of the naive Bayesian classifier on almost all databases analyzed, and hence is an enhancement of the naive Bayesian classifier. Relative to the non-selective Bayesian network classifier, our selective Bayesian network classifier generates networks that are computationally simpler to evaluate and that display predictive accuracy comparable to that of Bayesian networks which model all features. 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.

Paper #3222 has the title `Beyond Independence: Conditions for the Optimality of the Simple Bayesian Classifier  
` and the abstract `The simple Bayesian classifier (SBC) is commonly thought to assume that attributes are independent given the class, but this is apparently contradicted by the surprisingly good performance it exhibits in many domains that contain clear attribute dependences. No explanation for this has been proposed so far. In this paper we show that the SBC does not in fact assume attribute independence, and can be optimal even when this assumption is violated by a wide margin. The key to this finding lies in the distinction between classification and probability estimation: correct classification can be achieved even when the probability estimates used contain large errors. We show that the previously-assumed region of optimality of the SBC is a second-order infinitesimal fraction of the actual one. This is followed by the derivation of several necessary and several sufficient conditions for the optimality of the SBC. For example, the SBC is optimal for learning arbitrary conjunctions and disjunctions, even though they violate the independence assumption. The paper also reports empirical evidence of the SBC's competitive performance in domains containing substantial degrees of attribute dependence. 
`.
Question: Which category should Paper #3222 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #3222 has the title `Beyond Independence: Conditions for the Optimality of the Simple Bayesian Classifier  
` and the abstract `The simple Bayesian classifier (SBC) is commonly thought to assume that attributes are independent given the class, but this is apparently contradicted by the surprisingly good performance it exhibits in many domains that contain clear attribute dependences. No explanation for this has been proposed so far. In this paper we show that the SBC does not in fact assume attribute independence, and can be optimal even when this assumption is violated by a wide margin. The key to this finding lies in the distinction between classification and probability estimation: correct classification can be achieved even when the probability estimates used contain large errors. We show that the previously-assumed region of optimality of the SBC is a second-order infinitesimal fraction of the actual one. This is followed by the derivation of several necessary and several sufficient conditions for the optimality of the SBC. For example, the SBC is optimal for learning arbitrary conjunctions and disjunctions, even though they violate the independence assumption. The paper also reports empirical evidence of the SBC's competitive performance in domains containing substantial degrees of attribute dependence. 
`.
Question: Which category should Paper #3222 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: Case_Based