Results 11  20
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156
Small Sample Statistics for Classification Error Rates I: Error Rate Measurements
 Dept. of Inf. and Comp. Sci
, 1996
"... Several methods (independent subsamples, leaveoneout, crossvalidation, and bootstrapping) have been proposed for estimating the error rates of classifiers. The rationale behind the various estimators and the causes of the sometimes conflicting claims regarding their bias and precision are explore ..."
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Cited by 31 (1 self)
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Several methods (independent subsamples, leaveoneout, crossvalidation, and bootstrapping) have been proposed for estimating the error rates of classifiers. The rationale behind the various estimators and the causes of the sometimes conflicting claims regarding their bias and precision are explored in this paper. The biases and variances of each of the estimators are examined empirically. Crossvalidation, 10fold or greater, seems to be the best approach; the other methods are biased, have poorer precision, or are inconsistent. Though unbiased for linear discriminant classifiers, the 632b bootstrap estimator is biased for nearest neighbors classifiers, more so for single nearest neighbor than for three nearest neighbors. The 632b estimator is also biased for Cartstyle decision trees. Weiss' loo* estimator is unbiased and has better precision than crossvalidation for discriminant and nearest neighbors classifiers, but its lack of bias and improved precision for those classifiers do...
The interplay of bayesian and frequentist analysis
 Statist. Sci
, 2004
"... Statistics has struggled for nearly a century over the issue of whether the Bayesian or frequentist paradigm is superior. This debate is far from over and, indeed, should continue, since there are fundamental philosophical and pedagogical issues at stake. At the methodological level, however, the fi ..."
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Cited by 30 (0 self)
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Statistics has struggled for nearly a century over the issue of whether the Bayesian or frequentist paradigm is superior. This debate is far from over and, indeed, should continue, since there are fundamental philosophical and pedagogical issues at stake. At the methodological level, however, the fight has become considerably muted, with the recognition that each approach has a great deal to contribute to statistical practice and each is actually essential for full development of the other approach. In this article, we embark upon a rather idiosyncratic walk through some of these issues. Key words and phrases: Admissibility; Bayesian model checking; conditional frequentist; confidence intervals; consistency; coverage; design; hierarchical models; nonparametric
ModelBased Hierarchical Clustering
 In Proc. 16th Conf. Uncertainty in Artificial Intelligence
, 2000
"... We present an approach to modelbased hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex featureset partitioning that is a key component of our model. Features can have ei ..."
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Cited by 23 (0 self)
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We present an approach to modelbased hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex featureset partitioning that is a key component of our model. Features can have either a unique distribution in every cluster or a common distribution over some (or even all) of the clusters. The cluster subsets over which these features have such a common distribution correspond to the nodes (clusters) of the tree representing the hierarchy. We apply this general model to the problem of document clustering for which we use a multinomial likelihood function and Dirichlet priors. Our algorithm consists of a twostage process wherein we first perform a flat clustering followed by a modified hierarchical agglomerative merging process that includes determining the features that will have common distributions over the merged clusters. The regularization induced...
On Universal Prediction and Bayesian Confirmation
 Theoretical Computer Science
, 2007
"... The Bayesian framework is a wellstudied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not ..."
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Cited by 23 (12 self)
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The Bayesian framework is a wellstudied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not always available or can fail, in particular in complex situations. Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. I discuss in breadth how and in which sense universal (noni.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. I show that Solomonoff’s model possesses many desirable properties: Strong total and future bounds, and weak instantaneous bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the oldevidence and updating problem. It even performs well
Target tracking using a joint acoustic video system
 Department of Electrical and Computer Engineering, University of Maryland, College
, 2007
"... Abstract—In this paper, a multitarget tracking system for collocated video and acoustic sensors is presented. We formulate the tracking problem using a particle filter based on a statespace approach. We first discuss the acoustic statespace formulation whose observations use a sliding window of di ..."
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Cited by 18 (4 self)
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Abstract—In this paper, a multitarget tracking system for collocated video and acoustic sensors is presented. We formulate the tracking problem using a particle filter based on a statespace approach. We first discuss the acoustic statespace formulation whose observations use a sliding window of directionofarrival estimates. We then present the video state space that tracks a target’s position on the image plane based on online adaptive appearance models. For the joint operation of the filter, we combine the state vectors of the individual modalities and also introduce a timedelay variable to handle the acousticvideo data synchronization issue, caused by acoustic propagation delays. A novel particle filter proposal strategy for joint statespace tracking is introduced, which places the random support of the joint filter where the final posterior is likely to lie. By using the KullbackLeibler divergence measure, it is shown that the joint operation of the filter decreases the worst case divergence of the individual modalities. The resulting joint tracking filter is quite robust against video and acoustic occlusions due to our proposal strategy. Computer simulations are presented with synthetic and field data to demonstrate the filter’s performance. Index Terms—Acoustic tracking, multimodal data fusion, particle filtering, visual tracking. I.
An Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis
 Statistics and Computing
, 1991
"... The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rej ..."
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Cited by 18 (0 self)
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The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rejection method approach for implementation of the Gibbs sampler when nonconjugate structure is present. Several challenging applications are presented for illustration.
Strong matching for frequentist and Bayesian inference
 J. Statist. Plann. Inference
, 2002
"... inference ..."
Flexible covariance estimation in graphical Gaussian models
 ANNALS OF STATISTICS
, 2008
"... In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the WP G family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278–1323] we derive closedform expressions for Bayes estimat ..."
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Cited by 16 (3 self)
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In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the WP G family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278–1323] we derive closedform expressions for Bayes estimators under the entropy and squarederror losses. The WP G family includes the classical inverse of the hyper inverse Wishart but has many more shape parameters, thus allowing for flexibility in differentially shrinking various parts of the covariance matrix. Moreover, using this family avoids recourse to MCMC, often infeasible in highdimensional problems. We illustrate the performance of our estimators through a collection of numerical examples where we explore frequentist risk properties and the efficacy of graphs in the estimation of highdimensional covariance structures.
An introduction to Bayesian reference analysis: Inference on the ratio of multinomial parameters. The Statistician 47
, 1998
"... ..."
Coverage Probability Bias, Objective Bayes and the Likelihood Principle
 Biometrika
, 1999
"... this paper, the discussion focuses on the case of a single real parameter. ..."
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Cited by 14 (0 self)
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this paper, the discussion focuses on the case of a single real parameter.