Kilian Fatras

Abstract: Noisy labels often occur in vision datasets, especially when they are issued from crowdsourcing or Web scraping. In this paper, we propose a new regularization method which enables one to learn robust classifiers in presence of noisy data. To achieve this goal, we augment the virtual adversarial loss with a Wasserstein distance. This distance allows us to take into account specific relations between classes by leveraging on the geometric properties of this optimal transport distance. Notably, we encode the class similarities in the ground cost that is used to compute the Wasserstein distance. As a consequence, we can promote smoothness between classes that are very dissimilar, while keeping the classification decision function sufficiently complex for similar classes. While designing this ground cost can be left as a problem-specific modeling task, we show in this paper that using the semantic relations between classes names already leads to good results.Our proposed Wasserstein Adversarial Training (WAT) outperforms state of the art on four datasets corrupted with noisy labels: three classical benchmarks and one real case in remote sensing image semantic segmentation.

Abstract: Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity operator for the nonsmooth terms, which can be a costly operation for complex penalties. In this work we introduce two variance-reduced incremental methods based on SAGA and SVRG that can efficiently take into account complex penalties which can be expressed as a sum of proximal terms. This includes penalties such as total variation, group lasso with overlap and trend filtering, to name a few. Furthermore, we also develop sparse variants of the proposed algorithms which can take advantage of sparsity in the input data. Like other incremental methods, it only requires to evaluate the gradient of a single sample per iteration, and so is ideally suited for large scale applications. We provide a convergence rate analysis for the proposed methods and show that they converge with a fixed step-size, achieving in some cases the same asymptotic rate as their full gradient variants. Empirical benchmarks on 3 different datasets illustrate the practical advantages of the proposed methods.