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Author : Pi-yeong Chi
Publisher :
Page : 244 pages
File Size : 25,98 MB
Release : 1975
Category : Bayesian statistical decision theory
ISBN :
Author : B. L. S. Prakasa Rao
Publisher : Academic Press
Page : 539 pages
File Size : 20,70 MB
Release : 2014-07-10
Category : Mathematics
ISBN : 148326923X
Nonparametric Functional Estimation is a compendium of papers, written by experts, in the area of nonparametric functional estimation. This book attempts to be exhaustive in nature and is written both for specialists in the area as well as for students of statistics taking courses at the postgraduate level. The main emphasis throughout the book is on the discussion of several methods of estimation and on the study of their large sample properties. Chapters are devoted to topics on estimation of density and related functions, the application of density estimation to classification problems, and the different facets of estimation of distribution functions. Statisticians and students of statistics and engineering will find the text very useful.
Author : Hamed Masnadi-Shirazi
Publisher :
Page : 203 pages
File Size : 20,41 MB
Release : 2011
Category :
ISBN : 9781124703596
The combination of using loss functions that are both Bayes consistent and margin enforcing has lead to powerful classification algorithms such as AdaBoost that uses the exponential loss and logistic regression and LogitBoost that use the logistic loss. The use of Bayes consistent margin enforcing losses along with efficient optimization techniques has also lead to other successful classification algorithms such as SVM classifiers that use the hinge loss function. The success of boosting and SVM classifiers is not surprising when looked at from the standpoint of Bayes consistency. Such algorithms are all based on Bayes consistent loss functions and so are guaranteed to converge to the Bayes optimal decision rule as the number of training samples increases. Despite the importance and success of Bayes consistent loss functions, the number of such known loss functions has remained small in the literature. This is in part due to the fact that a generative method for deriving such loss functions did not exist. Not having a generative method for deriving Bayes consistent loss functions not only prevents one from effectively designing loss functions with certain shapes, but also prevents a full analysis and taxonomy of the possible shapes and properties that such loss function can have. In this thesis we solve these problems by providing a generative method for deriving Bayes consistent loss functions. We also fully analyze such loss functions and explore the design of loss functions with certain shapes and properties. This is achieved by studying and relating the two fields of risk minimization in machine learning and probability elicitation in statistics. Specifically, the class of Bayes consistent loss functions is partitioned into different varieties based on their convexity properties. The convexity properties of the loss and associated risk of Bayes consistent loss functions are also studied in detail which, for the first time, enable the derivation of non convex Bayes consistent loss functions. We also develop a fully constructive method for the derivation of novel canonical loss functions. This is due to a simple connection between the associated minimum conditional risk and optimal link functions. The added insight allows us to derive variable margin losses with explicit margin control. We then establish a common boosting framework, canonical gradientBoost, for building boosting classifiers from all canonical losses. Next, we extend the probability elicitation view of loss function design to the problem of designing robust loss functions for classification. The robust Savage loss and corresponding SavageBoost algorithm are derived and shown to outperform other boosting algorithms on a set of experiments designed to test the robustness of the algorithms to outliers in the training data. We also argue that a robust loss should penalizes both large positive and large negative margins. The Tangent loss and the associated TangentBoost classifier are derived with the desired robust properties. We also develop a general framework for the derivation of Bayes consistent cost sensitive loss functions. This is then used to derive a novel cost sensitive hinge loss function. A cost-sensitive SVM learning algorithm is then derived. Unlike previous SVM algorithms, the one now proposed is shown to enforce cost sensitivity for both separable and non-separable training data, independent of the choice of slack penalty. Finally, we present a novel framework for the design of cost-sensitive boosting algorithms. The proposed framework is used to derive cost-sensitive extensions of AdaBoost, RealBoost and LogitBoost. Experimental evidence, over different machine learning and computer vision problems is presented in support of the new algorithms.
Author : Gérard Biau
Publisher : Springer
Page : 284 pages
File Size : 36,43 MB
Release : 2015-12-08
Category : Mathematics
ISBN : 3319253883
This text presents a wide-ranging and rigorous overview of nearest neighbor methods, one of the most important paradigms in machine learning. Now in one self-contained volume, this book systematically covers key statistical, probabilistic, combinatorial and geometric ideas for understanding, analyzing and developing nearest neighbor methods. Gérard Biau is a professor at Université Pierre et Marie Curie (Paris). Luc Devroye is a professor at the School of Computer Science at McGill University (Montreal).
Author : Satosi Watanabe
Publisher : Academic Press
Page : 591 pages
File Size : 38,53 MB
Release : 2014-05-12
Category : Reference
ISBN : 1483268985
Methodologies of Pattern Recognition is a collection of papers that deals with the two approaches to pattern recognition (geometrical and structural), the Robbins-Monro procedures, and the implications of interactive graphic computers for pattern recognition methodology. Some papers describe non-supervised learning in statistical pattern recognition, parallel computation in pattern recognition, and statistical analysis as a tool to make patterns emerge from data. One paper points out the importance of cluster processing in visual perception in which proximate points of similar brightness values form clusters. At higher levels of mental activity humans are efficient in clumping complex items into clusters. Another paper suggests a recognition method which combines versatility and an efficient noise-proofness in dealing with the two main problems in the field of recognition. These difficulties are the presence of a large variety of observed signals and the presence of interference. One paper reports on a possible feature selection for pattern recognition systems employing the minimization of population entropy. Electronic engineers, physicists, physiologists, psychologists, logicians, mathematicians, and philosophers will find great rewards in reading the above collection.
Author : Milton Vernon Johns
Publisher :
Page : 22 pages
File Size : 44,51 MB
Release : 1959
Category :
ISBN :
The report considers the problem of classifying an individual into one of two categories in the non-parametric case. Classification procedures are proposed which make use of all observations previously taken on individuals independently selected from the same population. These procedures have risks which are asymptotically optimum as the number of prior observations becomes large. The loss due to misclassification is assumed to depend on the value of a random variable associated with the individual but not observed at the time of classification. The case where only one of the losses due to misclassification of individuals previously selected from the population is known is also, considered, and similar results are obtained. (Author).
Author : J.K. Ghosh
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 28,67 MB
Release : 2006-05-11
Category : Mathematics
ISBN : 0387226540
This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.
Author : Kenneth Abend
Publisher :
Page : 110 pages
File Size : 47,36 MB
Release : 1967
Category : Bayesian statistical decision theory
ISBN :
Compound decision theory is shown to be powerful as a general theoretical framework for pattern recognition, leading to nonparametric methods, methods of threshold adjustment, and methods for taking context into account. The finite-sample-size performance of the Fix-Hodges nearest-neighbor nonparametric classification procedure is derived for independent binary patterns. The optimum (Bayes) sequential compound decision procedure, for known distributions and dependent states of nature is derived. When the states of nature form a Markov chain, the procedure is recursive, easily implemented, and immediately applicable to the use of context. A similar procedure, in which a decision depends on previous observations only through the decision about the preceding state of nature, can (when the populations are not well separated) yield results significantly worse than a procedure that does not depend on previous observations at all. When the populations are well separated, however, an improvement almost equal to that of the optimum sequential rule is achieved. (Author)
Author : Subhashis Ghosal
Publisher : Cambridge University Press
Page : 671 pages
File Size : 19,65 MB
Release : 2017-06-26
Category : Business & Economics
ISBN : 0521878268
Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.
Author : W. J. Dixon
Publisher : Univ of California Press
Page : 576 pages
File Size : 28,76 MB
Release : 2023-12-22
Category : Computers
ISBN : 0520338219
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1974. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived