Constrained Convex Neyman-Pearson Classification Using an Outer Approximation Splitting Method

Michel Barlaud (1) , Patrick Louis Combettes (2) , Lionel Fillatre (3)

1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe IMAGES-CREATIVE
2 LJLL - Laboratoire Jacques-Louis Lions
3 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Projet MEDIACODING

This paper presents an algorithm for Neyman-Pearson classification. While empirical risk minimization approaches focus on minimizing a global risk, the Neyman-Pearson framework minimizes the type II risk under an upper bound constraint on the type I risk. Since the 0=1 loss function is not convex, optimization methods employ convex surrogates that lead to tractable minimization problems. As shown in recent work, statistical bounds can be derived to quantify the cost of using such surrogates instead of the exact 1/0 loss. However, no specific algorithm has yet been proposed to actually solve the resulting minimization problem numerically. The contribution of this paper is to propose an efficient splitting algorithm to address this issue. Our method alternates a gradient step on the objective surrogate risk and an approximate projection step onto the constraint set, which is implemented by means of an outer approximation subgradient projection algorithm. Experiments on both synthetic data and biological data show the efficiency of the proposed method.

Mots clés: Convex optimization; machine learning; calibrated risk; splitting algorithm

Domaines: Statistiques [stat]; Machine Learning [stat.ML]

Michel Barlaud, Patrick Louis Combettes, Lionel Fillatre. Constrained Convex Neyman-Pearson Classification Using an Outer Approximation Splitting Method. 2015. ⟨hal-01160831⟩