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Statistical learning theory

About: Statistical learning theory is a research topic. Over the lifetime, 1618 publications have been published within this topic receiving 158033 citations.


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TL;DR: This work combines the PAC-Bayes approach introduced by McAllester (1998), with the optimal union bound provided by the generic chaining technique developed by Fernique and Talagrand, in a way that also takes into account the variance of the combined functions.
Abstract: There exist many different generalization error bounds in statistical learning theory. Each of these bounds contains an improvement over the others for certain situations or algorithms. Our goal is, first, to underline the links between these bounds, and second, to combine the different improvements into a single bound. In particular we combine the PAC-Bayes approach introduced by McAllester (1998), which is interesting for randomized predictions, with the optimal union bound provided by the generic chaining technique developed by Fernique and Talagrand (see Talagrand, 1996), in a way that also takes into account the variance of the combined functions. We also show how this connects to Rademacher based bounds.

45 citations

Journal ArticleDOI
TL;DR: It is shown that the decision function obtained by C-SVC is just one of the decision functions obtained by solving the optimization problem derived directly from the structural risk minimization principle.
Abstract: This paper is concerned with the theoretical foundation of support vector machines (SVMs). The purpose is to develop further an exact relationship between SVMs and the statistical learning theory (SLT). As a representative, the standard C-support vector classification (C-SVC) is considered here. More precisely, we show that the decision function obtained by C-SVC is just one of the decision functions obtained by solving the optimization problem derived directly from the structural risk minimization principle. In addition, an interesting meaning of the parameter C in C-SVC is given by showing that C corresponds to the size of the decision function candidate set in the structural risk minimization principle.

45 citations

Journal ArticleDOI
TL;DR: In this article, the authors present eight PAC-Bayes bounds to analyze the generalization performance of multi-view classifiers, which are derived from two derived logarithmic determinant inequalities whose difference lies in whether the dimensionality of data is involved.

44 citations

Journal ArticleDOI
TL;DR: Support Vector Regression was applied to predict the cold modulus of sialon ceramic with satisfactory results and showed that the prediction accuracy of SVR model was higher than those of BP-ANN and PLS models.

44 citations

Journal ArticleDOI
TL;DR: This paper's models capture several state-of-the-art empirical and theoretical approaches to the problem, ranging from self-improving algorithms to empirical performance models, and the results identify conditions under which these approaches are guaranteed to perform well.
Abstract: The best algorithm for a computational problem generally depends on the “relevant inputs,” a concept that depends on the application domain and often defies formal articulation. While there is a large body of literature on empirical approaches to selecting the best algorithm for a given application domain, there has been surprisingly little theoretical analysis of the problem. This paper adapts concepts from statistical and online learning theory to reason about application-specific algorithm selection. Our models capture several state-of-the-art empirical and theoretical approaches to the problem, ranging from self-improving algorithms to empirical performance models, and our results identify conditions under which these approaches are guaranteed to perform well. We present one framework that models algorithm selection as a statistical learning problem, and our work here shows that dimension notions from statistical learning theory, historically used to measure the complexity of classes of binary- and re...

44 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20239
202219
202159
202069
201972
201847