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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Bibliographic Details
Published in:Annals of mathematics and artificial intelligence Vol. 88; no. 1-3; pp. 269 - 289
Main Authors: Couellan, Nicolas, Jan, Sophie
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2020
Springer
Springer Nature B.V
Springer Verlag
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-019-09676-0