Graph explorer

Gaussian Robust Classification

Supervised learning is all about the ability to generalize knowledge. Specifically, the goal of the learning is to train a classifier using training data, in such a way that it will be capable of classifying new unseen data correctly. In order to acheive this goal, it is important to carefully design the learner, so it will not overfit the training data. The later can is done usually by adding a regularization term. The statistical learning theory explains the success of this method by claiming that it restricts the complexity of the learned model. This explanation, however, is rather abstract and does not have a geometric intuition. The generalization error of a classifier may be thought of as correlated with its robustness to perturbations of the data: a classifier that copes with disturbance is expected to generalize well. Indeed, Xu et al. [2009] have shown that the SVM formulation is equivalent to a robust optimization (RO) formulation, in which an adversary displaces the training and testing points within a ball of pre-determined radius. In this work we explore a different kind of robustness, namely changing each data point with a Gaussian cloud centered at the sample. Loss i