A Convex Surrogate Operator for General Non-Modular Loss FunctionsReportar como inadecuado

A Convex Surrogate Operator for General Non-Modular Loss Functions - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

* Corresponding author 1 CVC - Center for Visual Computing 2 GALEN - Organ Modeling through Extraction, Representation and Understanding of Medical Image Content Inria Saclay - Ile de France, Ecole Centrale Paris 3 Departement Elektrotechniek - ESAT leuven

Abstract : Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, sub-modular functions or supermodular functions separately while maintaining polynomial time computation. In this work, a novel generic convex surrogate for general non-modular loss functions is introduced, which provides for the first time a tractable solution for loss functions that are neither super-modular nor submodular. This convex surro-gate is based on a submodular-supermodular decomposition for which the existence and uniqueness is proven in this paper. It takes the sum of two convex surrogates that separately bound the supermodular component and the submodular component using slack-rescaling and the Lovász hinge, respectively. It is further proven that this surrogate is convex , piecewise linear, an extension of the loss function, and for which subgradient computation is polynomial time. Empirical results are reported on a non-submodular loss based on the Sørensen-Dice difference function, and a real-world face track dataset with tens of thousands of frames, demonstrating the improved performance, efficiency, and scalabil-ity of the novel convex surrogate.

Autor: Jiaqian Yu - Matthew Blaschko -

Fuente: https://hal.archives-ouvertes.fr/


Documentos relacionados