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428
A Theory of Learning Classification Rules
, 1992
"... The main contributions of this thesis are a Bayesian theory of learning classification rules, the unification and comparison of this theory with some previous theories of learning, and two extensive applications of the theory to the problems of learning class probability trees and bounding error whe ..."
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Cited by 79 (6 self)
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The main contributions of this thesis are a Bayesian theory of learning classification rules, the unification and comparison of this theory with some previous theories of learning, and two extensive applications of the theory to the problems of learning class probability trees and bounding error when learning logical rules. The thesis is motivated by considering some current research issues in machine learning such as bias, overfitting and search, and considering the requirements placed on a learning system when it is used for knowledge acquisition. Basic Bayesian decision theory relevant to the problem of learning classification rules is reviewed, then a Bayesian framework for such learning is presented. The framework has three components: the hypothesis space, the learning protocol, and criteria for successful learning. Several learning protocols are analysed in detail: queries, logical, noisy, uncertain and positiveonly examples. The analysis is done by interpreting a protocol as a...
Plausibility Measures and Default Reasoning
 Journal of the ACM
, 1996
"... this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, fflsemantics, possibilistic structures, and rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. W ..."
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Cited by 79 (12 self)
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this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, fflsemantics, possibilistic structures, and rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:
Bayesian Treatment of the Independent Studentt Linear Model
 JOURNAL OF APPLIED ECONOMETRICS
, 1993
"... This article takes up methods for Bayesian inference in a linear model in which the disturbances are independent and have identical Studentt distributions. It exploits the equivalence of the Studentt distribution and an appropriate scale mixture of normals, and uses a Gibbs sampler to perform the ..."
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Cited by 74 (2 self)
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This article takes up methods for Bayesian inference in a linear model in which the disturbances are independent and have identical Studentt distributions. It exploits the equivalence of the Studentt distribution and an appropriate scale mixture of normals, and uses a Gibbs sampler to perform the computations. The new method is applied to some wellknown macroeconomic time series. It is found that posterior odds ratios favor the independent Studentt linear model over the normal linear model, and that the posterior odds ratio in favor of difference stationarity over trend stationarity is often substantially less in the favored Studentt models.
Bayesian Approaches to Gaussian Mixture Modelling
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... A Bayesianbased methodology is presented which automatically penalises overcomplex models being fitted to unknown data. We show that, with a Gaussian mixture model, the approach is able to select an `optimal' number of components in the model and so partition data sets. The performance of the Baye ..."
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Cited by 73 (2 self)
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A Bayesianbased methodology is presented which automatically penalises overcomplex models being fitted to unknown data. We show that, with a Gaussian mixture model, the approach is able to select an `optimal' number of components in the model and so partition data sets. The performance of the Bayesian method is compared to other methods of optimal model selection and found to give good results. The methods are tested on synthetic and real data sets. Introduction Scientific disciplines generate data. In the attempt to understand the patterns present in such data sets methods which perform some form of unsupervised partitioning or modelling are particularly useful. Such an approach is only of use, however, if it offers a less complex representation of the data than the data set itself. This introduces an apparent conflict, however, as any model improves its fit to the data monotonically with increases in its complexity (the number of model parameters)  a model as complex as the data...
Structure Learning in Conditional Probability Models via an Entropic Prior and Parameter Extinction
, 1998
"... We introduce an entropic prior for multinomial parameter estimation problems and solve for its maximum... ..."
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Cited by 66 (0 self)
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We introduce an entropic prior for multinomial parameter estimation problems and solve for its maximum...
Objective Bayesian Analysis of Spatially Correlated Data
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2000
"... Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly specified to be of a certain form (e.g., spherical, power exponential, rational quadratic, or Matérn) wi ..."
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Cited by 52 (7 self)
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Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly specified to be of a certain form (e.g., spherical, power exponential, rational quadratic, or Matérn) with a small number of unknown parameters. We consider objective Bayesian analysis of such spatial models, when the mean function of the Gaussian random field is specified as in a linear model. It is thus necessary to determine an objective (or default) prior distribution for the unknown mean and covariance parameters of the random field. We first
Expectations, Learning and Macroeconomic Persistence
 Journal of Monetary Economics
, 2007
"... Abstract. This paper presents an estimated model with learning and provides evidence that learning can improve the …t of popular monetary DSGE models and endogenously generate realistic levels of persistence. The paper starts with an agnostic view, developing a model that nests learning and some of ..."
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Cited by 52 (2 self)
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Abstract. This paper presents an estimated model with learning and provides evidence that learning can improve the …t of popular monetary DSGE models and endogenously generate realistic levels of persistence. The paper starts with an agnostic view, developing a model that nests learning and some of the structural sources of persistence, such as habit formation in consumption and in‡ation indexation, that are typically needed in monetary models with rational expectations to match the persistence of macroeconomic variables. I estimate the model by likelihoodbased Bayesian methods, which allow the estimation of the learning gain coe ¢ cient jointly with the ‘deep’parameters of the economy. The empirical results show that when learning replaces rational expectations, the estimated degrees of habits and indexation drop near zero. This …nding suggests that persistence arises in the model economy mainly from expectations and learning. The posterior model probabilities show that the speci…cation with learning …ts signi…cantly better than does the speci…cation with rational expectations. Finally, if learning rather than mechanical sources of persistence provides a more appropriate representation of the economy, the implied optimal policy will be di¤erent. The policymaker will
From Laplace To Supernova Sn 1987a: Bayesian Inference In Astrophysics
, 1990
"... . The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions ..."
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Cited by 51 (2 self)
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. The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions to wellposed statistical problems, and is historically the original approach to statistics. The reasons for earlier rejection of Bayesian methods are discussed, and it is noted that the work of Cox, Jaynes, and others answers earlier objections, giving Bayesian inference a firm logical and mathematical foundation as the correct mathematical language for quantifying uncertainty. The Bayesian approaches to parameter estimation and model comparison are outlined and illustrated by application to a simple problem based on the gaussian distribution. As further illustrations of the Bayesian paradigm, Bayesian solutions to two interesting astrophysical problems are outlined: the measurement of wea...