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

Nicolas Couellan (1, 2) , Sophie Jan (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ENAC - Ecole Nationale de l'Aviation Civile

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 techniques are based on Random Fourier Features and the Nyström methods. The resulting formulations can be solved with efficient stochastic approximation techniques such as stochastic (sub)-gradient, stochastic proximal gradient techniques or their variants.

Domaines: Apprentissage [cs.LG]; Machine Learning [stat.ML]; Optimisation et contrôle [math.OC]

Nicolas Couellan, Sophie Jan. Feature uncertainty bounds for explicit feature maps and large robust nonlinear SVM classifiers. Annals of Mathematics and Artificial Intelligence, 2020, 88 (1-3), pp.269-289. ⟨10.1007/s10472-019-09676-0⟩. ⟨hal-01718729⟩