Uncertainty-safe large scale support vector machines

The issue of large scale binary classification when data is subject to random perturbations is addressed. The proposed model integrates a learning framework that adjusts its robustness to noise during learning. The method avoids over-conservative situations that can be encountered with worst-case robust support vector machine formulations. The algorithm could be seen as a technique to learn the support-set of the noise distribution during the training process. This is achieved by introducing optimization variables that control the magnitude of the noise perturbations that should be taken into account. The magnitude is tuned by optimizing a generalization error. Only rough estimates of perturbations bounds are required. Additionally, a stochastic bi-level optimization technique is proposed to solve the resulting formulation. The algorithm performs very cheap stochastic subgradient moves and is therefore well suited to large datasets. Encouraging experimental results show that the technique outperforms robust second order cone programming formulations.