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215,118
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vec ..."
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Cited by 958 (5 self)
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This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance
Bayesian Interpolation
 Neural Computation
, 1991
"... Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. T ..."
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Cited by 721 (17 self)
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Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data
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 788 (23 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
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
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Cited by 741 (23 self)
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We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties
Bayesian Data Analysis
, 1995
"... I actually own a copy of Harold Jeffreys’s Theory of Probability but have only read small bits of it, most recently over a decade ago to confirm that, indeed, Jeffreys was not too proud to use a classical chisquared pvalue when he wanted to check the misfit of a model to data (Gelman, Meng and Ste ..."
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Cited by 2132 (59 self)
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I actually own a copy of Harold Jeffreys’s Theory of Probability but have only read small bits of it, most recently over a decade ago to confirm that, indeed, Jeffreys was not too proud to use a classical chisquared pvalue when he wanted to check the misfit of a model to data (Gelman, Meng and Stern, 2006). I do, however, feel that it is important to understand where our probability models come from, and I welcome the opportunity to use the present article by Robert, Chopin and Rousseau as a platform for further discussion of foundational issues. 2 In this brief discussion I will argue the following: (1) in thinking about prior distributions, we should go beyond Jeffreys’s principles and move toward weakly informative priors; (2) it is natural for those of us who work in social and computational sciences to favor complex models, contra Jeffreys’s preference for simplicity; and (3) a key generalization of Jeffreys’s ideas is to explicitly include model checking in the process of data analysis.
A Bayesian method for the induction of probabilistic networks from data
 MACHINE LEARNING
, 1992
"... This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computerassisted hypothesis testing, automated scientific discovery, and automated construction of probabili ..."
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Cited by 1381 (32 self)
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This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computerassisted hypothesis testing, automated scientific discovery, and automated construction
A Practical Bayesian Framework for Backprop Networks
 Neural Computation
, 1991
"... A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures ..."
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Cited by 496 (20 self)
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A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures
Estimating Continuous Distributions in Bayesian Classifiers
 In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence
, 1995
"... When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated by a single Gaussian. In this paper we abandon the normality ..."
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Cited by 489 (2 self)
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distribution with a single Gaussian; and using nonparametric kernel density estimation. We observe large reductions in error on several natural and artificial data sets, which suggests that kernel estimation is a useful tool for learning Bayesian models. In Proceedings of the Eleventh Conference on Uncertainty
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 930 (41 self)
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In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
Results 1  10
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