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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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Journal ArticleDOI
TL;DR: A characterization of linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy shows that overparameterization is essential for benign overfitting in this setting: the number of directions in parameter space that are unimportant for prediction must significantly exceed the sample size.
Abstract: The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider when a perfect fit to training data in linear regression is compatible with accurate prediction. We give a characterization of linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy. The characterization is in terms of two notions of the effective rank of the data covariance. It shows that overparameterization is essential for benign overfitting in this setting: the number of directions in parameter space that are unimportant for prediction must significantly exceed the sample size. By studying examples of data covariance properties that this characterization shows are required for benign overfitting, we find an important role for finite-dimensional data: the accuracy of the minimum norm interpolating prediction rule approaches the best possible accuracy for a much narrower range of properties of the data distribution when the data lie in an infinite-dimensional space vs. when the data lie in a finite-dimensional space with dimension that grows faster than the sample size.

482 citations

Journal ArticleDOI
TL;DR: A Python-based, cross-platform, and open-source software toolbox, called PyMVPA, for the application of classifier-based analysis techniques to fMRI datasets, which makes use of Python’s ability to access libraries written in a large variety of programming languages and computing environments to interface with the wealth of existing machine learning packages.
Abstract: Decoding patterns of neural activity onto cognitive states is one of the central goals of functional brain imaging. Standard univariate fMRI analysis methods, which correlate cognitive and perceptual function with the blood oxygenation-level dependent (BOLD) signal, have proven successful in identifying anatomical regions based on signal increases during cognitive and perceptual tasks. Recently, researchers have begun to explore new multivariate techniques that have proven to be more flexible, more reliable, and more sensitive than standard univariate analysis. Drawing on the field of statistical learning theory, these new classifier-based analysis techniques possess explanatory power that could provide new insights into the functional properties of the brain. However, unlike the wealth of software packages for univariate analyses, there are few packages that facilitate multivariate pattern classification analyses of fMRI data. Here we introduce a Python-based, cross-platform, and open-source software toolbox, called PyMVPA, for the application of classifier-based analysis techniques to fMRI datasets. PyMVPA makes use of Python’s ability to access libraries written in a large variety of programming languages and computing environments to interface with the wealth of existing machine learning packages. We present the framework in this paper and provide illustrative examples on its usage, features, and programmability.

480 citations

Journal ArticleDOI
TL;DR: An improved version of the TBSVM is proposed, named twin bounded support vector machines (TBSVM), based on TWSVM, that the structural risk minimization principle is implemented by introducing the regularization term.
Abstract: For classification problems, the generalized eigenvalue proximal support vector machine (GEPSVM) and twin support vector machine (TWSVM) are regarded as milestones in the development of the powerful SVMs, as they use the nonparallel hyperplane classifiers. In this brief, we propose an improved version, named twin bounded support vector machines (TBSVM), based on TWSVM. The significant advantage of our TBSVM over TWSVM is that the structural risk minimization principle is implemented by introducing the regularization term. This embodies the marrow of statistical learning theory, so this modification can improve the performance of classification. In addition, the successive overrelaxation technique is used to solve the optimization problems to speed up the training procedure. Experimental results show the effectiveness of our method in both computation time and classification accuracy, and therefore confirm the above conclusion further.

476 citations

Journal ArticleDOI
TL;DR: The support vector machine, a novel artificial intelligence-based method developed from statistical learning theory, is adopted herein to establish a real-time stage forecasting model that can effectively predict the flood stage forecasts one-to-six-hours ahead.

464 citations

Journal ArticleDOI
TL;DR: An overview of the SVM, both one-class and two-class SVM methods, is first presented followed by its use in landslide susceptibility mapping, where it is concluded that two- class SVM possesses better prediction efficiency than logistic regression and one- Class SVM.

450 citations


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