Minimisation du risque empirique avec des fonctions de perte nonmodulaires

Abstract : This thesis addresses the problem of learning with non-modular losses. In a prediction problem where multiple outputs are predicted simultaneously, viewing the outcome as a joint set prediction is essential so as to better incorporate real-world circumstances. In empirical risk minimization, we aim at minimizing an empirical sum over losses incurred on the finite sample with some loss function that penalizes on the prediction given the ground truth. In this thesis, we propose tractable and efficient methods for dealing with non-modular loss functions with correctness and scalability validated by empirical results. First, we present the hardness of incorporating supermodular loss functions into the inference term when they have different graphical structures. We then introduce an alternating direction method of multipliers (ADMM) based decomposition method for loss augmented inference, that only depends on two individual solvers for the loss function term and for the inference term as two independent subproblems. Second, we propose a novel surrogate loss function for submodular losses, the Lovász hinge, which leads to O(p log p) complexity with O(p) oracle accesses to the loss function to compute a subgradient or cutting-plane. Finally, we introduce a novel convex surrogate operator for general non-modular loss functions, which provides for the first time a tractable solution for loss functions that are neither supermodular nor submodular. This surrogate is based on a canonical submodular-supermodular decomposition.
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Jiaqian Yu. Minimisation du risque empirique avec des fonctions de perte nonmodulaires. Autre. Université Paris-Saclay, 2017. Français. ⟨NNT : 2017SACLC012⟩. ⟨tel-01514162⟩

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