Feature uncertainty bounds for explicit feature maps and large robust nonlinear SVM classifiers

We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertai...

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Vydané v:	Annals of mathematics and artificial intelligence Ročník 88; číslo 1-3; s. 269 - 289
Hlavní autori:	Couellan, Nicolas, Jan, Sophie
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cham Springer International Publishing 01.03.2020 Springer Springer Nature B.V Springer Verlag
Predmet:	Analysis Approximation Artificial Intelligence Classification Complex Systems Computer Science Datasets Feature maps Machine Learning Mathematics Numerical methods Optimization Optimization and Control Robustness (mathematics) Statistics Support vector machines Uncertainty Nyström method Support vector machines Random Fourier features 68T99 Robust optimization 90C25 Machine learning Robust classification 62G35
ISSN:	1012-2443, 1573-7470
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Popis
Shrnutí:	We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertainties associated to random approximate features in low dimensional spaces. The proposed bound calculations are based on Random Fourier Features and the Nyström methods. Numerical experiments are conducted to illustrate the benefit of the technique. We also emphasize the decomposable structure of the proposed robust nonlinear formulation that allows the use of efficient stochastic approximation techniques when datasets are large.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1012-2443 1573-7470
DOI:	10.1007/s10472-019-09676-0