Topic
Bayesian programming
About: Bayesian programming is a research topic. Over the lifetime, 1083 publications have been published within this topic receiving 59164 citations.
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TL;DR: Tree Augmented Naive Bayes (TAN) is single out, which outperforms naive Bayes, yet at the same time maintains the computational simplicity and robustness that characterize naive Baye.
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 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.
4,775 citations
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01 Jan 2001TL;DR: The book introduces probabilistic graphical models and decision graphs, including Bayesian networks and influence diagrams, and presents a thorough introduction to state-of-the-art solution and analysis algorithms.
Abstract: Probabilistic graphical models and decision graphs are powerful modeling tools for reasoning and decision making under uncertainty. As modeling languages they allow a natural specification of problem domains with inherent uncertainty, and from a computational perspective they support efficient algorithms for automatic construction and query answering. This includes belief updating, finding the most probable explanation for the observed evidence, detecting conflicts in the evidence entered into the network, determining optimal strategies, analyzing for relevance, and performing sensitivity analysis. The book introduces probabilistic graphical models and decision graphs, including Bayesian networks and influence diagrams. The reader is introduced to the two types of frameworks through examples and exercises, which also instruct the reader on how to build these models. The book is a new edition of Bayesian Networks and Decision Graphs by Finn V. Jensen. The new edition is structured into two parts. The first part focuses on probabilistic graphical models. Compared with the previous book, the new edition also includes a thorough description of recent extensions to the Bayesian network modeling language, advances in exact and approximate belief updating algorithms, and methods for learning both the structure and the parameters of a Bayesian network. The second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision processes and partially ordered decision problems. The authors also provide a well-founded practical introduction to Bayesian networks, object-oriented Bayesian networks, decision trees, influence diagrams (and variants hereof), and Markov decision processes. give practical advice on the construction of Bayesian networks, decision trees, and influence diagrams from domain knowledge. give several examples and exercises exploiting computer systems for dealing with Bayesian networks and decision graphs. present a thorough introduction to state-of-the-art solution and analysis algorithms. The book is intended as a textbook, but it can also be used for self-study and as a reference book.
4,566 citations
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TL;DR: This paper presents a Bayesian method for constructing probabilistic networks from databases, focusing on constructing Bayesian belief networks, and extends the basic method to handle missing data and hidden variables.
Abstract: This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.
3,971 citations
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15 May 1996TL;DR: Approaches for Statistical Inference: The Bayes Approach, Model Criticism and Selection, and Performance of Bayes Procedures.
Abstract: Approaches for Statistical Inference. The Bayes Approach. The Empirical Bayes Approach. Performance of Bayes Procedures. Bayesian Computation. Model Criticism and Selection. Special Methods and Models. Case Studies. Appendices.
2,413 citations
IBM1
TL;DR: This work analyzes the impact of the distribution entropy on the classification error, showing that low-entropy feature distributions yield good performance of naive Bayes and demonstrates that naive Baye works well for certain nearlyfunctional feature dependencies.
Abstract: The naive Bayes classifier greatly simplify learning by assuming that features are independent given class. Although independence is generally a poor assumption, in practice naive Bayes often competes well with more sophisticated classifiers. Our broad goal is to understand the data characteristics which affect the performance of naive Bayes. Our approach uses Monte Carlo simulations that allow a systematic study of classification accuracy for several classes of randomly generated problems. We analyze the impact of the distribution entropy on the classification error, showing that low-entropy feature distributions yield good performance of naive Bayes. We also demonstrate that naive Bayes works well for certain nearlyfunctional feature dependencies, thus reaching its best performance in two opposite cases: completely independent features (as expected) and functionally dependent features (which is surprising). Another surprising result is that the accuracy of naive Bayes is not directly correlated with the degree of feature dependencies measured as the classconditional mutual information between the features. Instead, a better predictor of naive Bayes accuracy is the amount of information about the class that is lost because of the independence assumption.
2,046 citations