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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 short review describes mathematical techniques for statistical analysis and prediction in dynamical systems, and discusses how ideas from from operator-theoretic ergodic theory combined with statistical learning theory provide an effective route to address problems, leading to methods well-adapted to handle nonlinear dynamics.
Abstract: This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning problem of forecasting the time evolution of an observable under potentially incomplete observations at forecast initialization; and (ii) the unsupervised learning problem of identification of observables of the system with a coherent dynamical evolution. We discuss how ideas from from operator-theoretic ergodic theory combined with statistical learning theory provide an effective route to address these problems, leading to methods well-adapted to handle nonlinear dynamics, with convergence guarantees as the amount of training data increases.

13 citations

Proceedings Article
01 Jan 2001
TL;DR: The authors discusses the statistical theory underlying various parameter-estimation methods, and gives algorithms which depend on alternatives to (smoothed) maximum-likelihood estimation, and shows how important concepts from the classification literature - specifically, generalization results based on margins on training data - can be derived for parsing models.
Abstract: A fundamental problem in statistical parsing is the choice of criteria and algo-algorithms used to estimate the parameters in a model. The predominant approach in computational linguistics has been to use a parametric model with some variant of maximum-likelihood estimation. The assumptions under which maximum-likelihood estimation is justified are arguably quite strong. This chapter discusses the statistical theory underlying various parameter-estimation methods, and gives algorithms which depend on alternatives to (smoothed) maximum-likelihood estimation. We first give an overview of results from statistical learning theory. We then show how important concepts from the classification literature - specifically, generalization results based on margins on training data - can be derived for parsing models. Finally, we describe parameter estimation algorithms which are motivated by these generalization bounds.

13 citations

Journal ArticleDOI
TL;DR: The results showed that the normalization methods could affect the prediction performance of support vector machines and could be useful for determining a proper normalization method to achieve the best performance in SVMs.
Abstract: Support vector machines (SVM) based on the statistical learning theory is currently one of the most popular and efficient approaches for pattern recognition problem, because of their remarkable performance in terms of prediction accuracy. It is, however, required to choose a proper normalization method for input vectors in order to improve the system performance. Various normalization methods for SVMs have been studied in this research and the results showed that the normalization methods could affect the prediction performance. The results could be useful for determining a proper normalization method to achieve the best performance in SVMs.

13 citations

Proceedings ArticleDOI
20 Dec 2008
TL;DR: The proposed PSO-SVM model is applied to fault diagnosis of turbo-generator, among which PSO is used to determine free parameters of support vector machine, and is validated by the results of fault diagnosis examples.
Abstract: Support vector machine (SVM) is a new machine learning method based on statistical learning theory, which is a powerful tool for solving the problem with small sample, nonlinear and high dimension. However, the practicability of SVM is affected due to the difficulty of selecting appropriate SVM parameters. Particle swarm optimization (PSO) is a new optimization method, which is motivated by social behavior of bird flocking or fish schooling. The optimization method not only has strong global search capability, but also is very easy to implement. Thus, in the study, the proposed PSO-SVM model is applied to fault diagnosis of turbo-generator, among which PSO is used to determine free parameters of support vector machine. Finally, the effectiveness and correctness of this method are validated by the results of fault diagnosis examples. Consequently, PSO-SVM is a proper method in fault diagnosis of turbo-generator.

13 citations

Journal Article
TL;DR: In this paper, a new and improved characterization of the label complexity of disagreement-based active learning is introduced, in which the leading quantity is the version space compression set size, defined as the smallest subset of the training data that induces the same version space.
Abstract: We introduce a new and improved characterization of the label complexity of disagreement-based active learning, in which the leading quantity is the version space compression set size. This quantity is defined as the size of the smallest subset of the training data that induces the same version space. We show various applications of the new characterization, including a tight analysis of CAL and refined label complexity bounds for linear separators under mixtures of Gaussians and axis-aligned rectangles under product densities. The version space compression set size, as well as the new characterization of the label complexity, can be naturally extended to agnostic learning problems, for which we show new speedup results for two well known active learning algorithms.

13 citations


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