%0 Generic %1 blondel2018learning %A Blondel, Mathieu %A Martins, André F. T. %A Niculae, Vlad %D 2018 %K Fenchel-Young_losses classification optimization structured_sparsity %T Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms. %U http://arxiv.org/abs/1805.09717 %X We study in this paper Fenchel-Young losses, a generic way to construct convex loss functions from a convex regularizer. We provide an in-depth study of their properties in a broad setting and show that they unify many well-known loss functions. When constructed from a generalized entropy, which includes well-known entropies such as Shannon and Tsallis entropies, we show that Fenchel-Young losses induce a predictive probability distribution and develop an efficient algorithm to compute that distribution for separable entropies. We derive conditions for generalized entropies to yield a distribution with sparse support and losses with a separation margin. Finally, we present both primal and dual algorithms to learn predictive models with generic Fenchel-Young losses.

@misc{blondel2018learning, abstract = {We study in this paper Fenchel-Young losses, a generic way to construct convex loss functions from a convex regularizer. We provide an in-depth study of their properties in a broad setting and show that they unify many well-known loss functions. When constructed from a generalized entropy, which includes well-known entropies such as Shannon and Tsallis entropies, we show that Fenchel-Young losses induce a predictive probability distribution and develop an efficient algorithm to compute that distribution for separable entropies. We derive conditions for generalized entropies to yield a distribution with sparse support and losses with a separation margin. Finally, we present both primal and dual algorithms to learn predictive models with generic Fenchel-Young losses.}, added-at = {2018-12-07T10:22:56.000+0100}, author = {Blondel, Mathieu and Martins, André F. T. and Niculae, Vlad}, biburl = {https://www.bibsonomy.org/bibtex/2e835f0aecd3828dca9888c3ea2997f1f/jpvaldes}, description = {[1805.09717] Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms}, interhash = {7c005778347ea5ddcacac9c8ff98199b}, intrahash = {e835f0aecd3828dca9888c3ea2997f1f}, keywords = {Fenchel-Young_losses classification optimization structured_sparsity}, note = {cite arxiv:1805.09717}, timestamp = {2018-12-07T10:22:56.000+0100}, title = {Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms.}, url = {http://arxiv.org/abs/1805.09717}, year = 2018 }