The Strength of Weak Learnability
Machine Learning
Neural Networks - 2003 Special issue: Advances in neural networks research IJCNN'03
Convex Optimization
Probabilistically Constrained Linear Programs and Risk-Adjusted Controller Design
SIAM Journal on Optimization
Convex Approximations of Chance Constrained Programs
SIAM Journal on Optimization
Semi-Supervised Novelty Detection
The Journal of Machine Learning Research
A Neyman-Pearson approach to statistical learning
IEEE Transactions on Information Theory
Performance Measures for Neyman–Pearson Classification
IEEE Transactions on Information Theory
A plug-in approach to neyman-pearson classification
The Journal of Machine Learning Research
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Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss φ. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i) its φ-type I error is below a pre-specified level and (ii), it has φ-type II error close to the minimum possible. The proposed classifier is obtained by minimizing an empirical convex objective with an empirical convex constraint. The novelty of the method is that the classifier output by this computationally feasible program is shown to satisfy the original constraint on type I error. New techniques to handle such problems are developed and they have consequences on chance constrained programming. We also evaluate the price to pay in terms of type II error for being conservative on type I error.