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34
On the optimality of the simple Bayesian classifier under zeroone loss
 MACHINE LEARNING
, 1997
"... The simple Bayesian classifier is known to be optimal when attributes are independent given the class, but the question of whether other sufficient conditions for its optimality exist has so far not been explored. Empirical results showing that it performs surprisingly well in many domains containin ..."
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Cited by 601 (25 self)
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The simple Bayesian classifier is known to be optimal when attributes are independent given the class, but the question of whether other sufficient conditions for its optimality exist has so far not been explored. Empirical results showing that it performs surprisingly well in many domains containing clear attribute dependences suggest that the answer to this question may be positive. This article shows that, although the Bayesian classifier’s probability estimates are only optimal under quadratic loss if the independence assumption holds, the classifier itself can be optimal under zeroone loss (misclassification rate) even when this assumption is violated by a wide margin. The region of quadraticloss optimality of the Bayesian classifier is in fact a secondorder infinitesimal fraction of the region of zeroone optimality. This implies that the Bayesian classifier has a much greater range of applicability than previously thought. For example, in this article it is shown to be optimal for learning conjunctions and disjunctions, even though they violate the independence assumption. Further, studies in artificial domains show that it will often outperform more powerful classifiers for common training set sizes and numbers of attributes, even if its bias is a priori much less appropriate to the domain. This article’s results also imply that detecting attribute dependence is not necessarily the best way to extend the Bayesian classifier, and this is also verified empirically.
Bayesian Network Classifiers
, 1997
"... 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 stateoftheart classifiers such as C4.5. This fact raises the question of whether a classifier with less restr ..."
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Cited by 594 (22 self)
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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 stateoftheart 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 evaluate approaches for inducing classifiers from data, based on the theory of learning Bayesian networks. These networks are factored representations of probability distributions that generalize the naive Bayesian 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 that characterize naive Bayes. We experimentally tested these approaches, using problems from the University of California at Irvine repository, and compared them to C4.5, naive Bayes, and wrapper methods for feature selection.
Selection of relevant features and examples in machine learning
 ARTIFICIAL INTELLIGENCE
, 1997
"... In this survey, we review work in machine learning on methods for handling data sets containing large amounts of irrelevant information. We focus on two key issues: the problem of selecting relevant features, and the problem of selecting relevant examples. We describe the advances that have been mad ..."
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Cited by 427 (1 self)
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In this survey, we review work in machine learning on methods for handling data sets containing large amounts of irrelevant information. We focus on two key issues: the problem of selecting relevant features, and the problem of selecting relevant examples. We describe the advances that have been made on these topics in both empirical and theoretical work in machine learning, and we present a general framework that we use to compare different methods. We close with some challenges for future work in this area.
Hierarchically Classifying Documents Using Very Few Words
, 1997
"... The proliferation of topic hierarchies for text documents has resulted in a need for tools that automatically classify new documents within such hierarchies. Existing classification schemes which ignore the hierarchical structure and treat the topics as separate classes are often inadequate in text ..."
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Cited by 421 (9 self)
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The proliferation of topic hierarchies for text documents has resulted in a need for tools that automatically classify new documents within such hierarchies. Existing classification schemes which ignore the hierarchical structure and treat the topics as separate classes are often inadequate in text classification where the there is a large number of classes and a huge number of relevant features needed to distinguish between them. We propose an approach that utilizes the hierarchical topic structure to decompose the classification task into a set of simpler problems, one at each node in the classification tree. As we show, each of these smaller problems can be solved accurately by focusing only on a very small set of features, those relevant to the task at hand. This set of relevant features varies widely throughout the hierarchy, so that, while the overall relevant feature set may be large, each classifier only examines a small subset. The use of reduced feature sets allows us to util...
Comparing Bayesian Network Classifiers
, 1999
"... In this paper, we empirically evaluate algorithms for learning four types of Bayesian network (BN) classifiers  NaïveBayes, tree augmented NaïveBayes, BN augmented NaïveBayes and general BNs, where the latter two are learned using two variants of a conditionalindependence (CI) based BNlearnin ..."
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Cited by 80 (6 self)
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In this paper, we empirically evaluate algorithms for learning four types of Bayesian network (BN) classifiers  NaïveBayes, tree augmented NaïveBayes, BN augmented NaïveBayes and general BNs, where the latter two are learned using two variants of a conditionalindependence (CI) based BNlearning algorithm. Experimental results show the obtained classifiers, learned using the CI based algorithms, are competitive with (or superior to) the best known classifiers, based on both Bayesian networks and other formalisms; and that the computational time for learning and using these classifiers is relatively small. Moreover, these results also suggest a way to learn yet more effective classifiers; we demonstrate empirically that this new algorithm does work as expected. Collectively, these results argue that BN classifiers deserve more attention in machine learning and data mining communities. 1 INTRODUCTION Many tasks  including fault diagnosis, pattern recognition and forecasting  c...
Lazy Learning of Bayesian Rules
 Machine Learning
, 2000
"... The naive Bayesian classifier provides a simple and e#ective approach to classifier learning, but its attribute independence assumption is often violated in the real world. A number of approaches have sought to alleviate this problem. A Bayesian tree learning algorithm builds a decision tree, and ge ..."
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Cited by 39 (8 self)
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The naive Bayesian classifier provides a simple and e#ective approach to classifier learning, but its attribute independence assumption is often violated in the real world. A number of approaches have sought to alleviate this problem. A Bayesian tree learning algorithm builds a decision tree, and generates a local naive Bayesian classifier at each leaf. The tests leading to a leaf can alleviate attribute interdependencies for the local naive Bayesian classifier. However, Bayesian tree learning still su#ers from the small disjunct problem 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 the application of lazy learning techniques to Bayesian tree induction and presents the resulting lazy Bayesian rule learning algorithm, called Lbr. This algorithm can be justified by a variant of Bayes theorem which supports a weaker conditional attribute independence assumption than is required by naive Bayes. For each test example, it builds a most appropriate rule with a local naive Bayesian classifier as its consequent. It is demonstrated that the computational requirements of Lbr are reasonable in a wide crosssection of natural domains. Experiments with these domains show that, on average, this new algorithm obtains lower error rates significantly more often than the reverse in comparison to a naive Bayesian classifier, C4.5, a Bayesian tree learning algorithm, a constructive Bayesian classifier that eliminates attributes and constructs new attributes using Cartesian products of existing nominal attributes, and a lazy decision tree learning algorithm. It also outperforms, although the result is not statisticall...
Learning Probabilistic Networks
 THE KNOWLEDGE ENGINEERING REVIEW
, 1998
"... A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combini ..."
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Cited by 37 (1 self)
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A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combining prior knowledge, which might be limited solely to experience of the influences between some of the variables of interest, and data. In this paper, we first show how data can be used to revise initial estimates of the parameters of a model. We then progress to showing how the structure of the model can be revised as data is obtained. Techniques for learning with incomplete data are also covered.
Learning Goal Oriented Bayesian Networks for Telecommunications Risk Management
 In Proceedings of the 13th International Conference on Machine Learning
, 1996
"... This paper discusses issues related to Bayesian network model learning for unbalanced binary classification tasks. In general, the primary focus of current research on Bayesian network learning systems (e.g., K2 and its variants) is on the creation of the Bayesian network structure that fits the dat ..."
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Cited by 29 (0 self)
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This paper discusses issues related to Bayesian network model learning for unbalanced binary classification tasks. In general, the primary focus of current research on Bayesian network learning systems (e.g., K2 and its variants) is on the creation of the Bayesian network structure that fits the database best. It turns out that when applied with a specific purpose in mind, such as classification, the performance of these network models may be very poor. We demonstrate that Bayesian network models should be created to meet the specific goal or purpose intended for the model. We first present a goaloriented algorithm for constructing Bayesian networks for predicting uncollectibles in telecommunications riskmanagement datasets. Second, we argue and demonstrate that current Bayesian network learning methods may fail to perform satisfactorily in real life applications since they do not learn models tailored to a specific goal or purpose. Third, we discuss the performance of "goal oriented"...
A Comparison of Induction Algorithms for Selective and nonSelective Bayesian Classifiers
 Proceedings of the Twelfth International Conference on Machine Learning
, 1995
"... 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, highpredictiveaccu ..."
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Cited by 24 (5 self)
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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, highpredictiveaccuracy networks. We compare the performance of this classifier with selective and nonselective 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 nonselective 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. 1 INTRODUCTION Bayesian induction methods have proven to be an important cla...