General framework for binary classification on top samples. (3rd September 2022)

• Record Type: Journal Article
• Authors: Adam, L.; Mácha, V.; Šmídl, V.; Pevný, T.
• Is Part Of: Optimization methods and software. Volume 37:Number 5(2022)
• Page Start: 1636
• Page End: 1667
• Publication Date: 2022-09-03
• Subjects: General framework -- classification -- ranking -- accuracy at the top -- Neyman–Pearson -- Pat&Mat; 90C20 -- 49M05 -- 65K10 -- 49K10; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2021.1965601
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top, or hypothesis testing may be written in this form. We propose a general framework to handle these classes of problems and show which formulations (both known and newly proposed) fall into this framework. We provide a theoretical analysis of this framework and mention selected possible pitfalls the formulations may encounter. We show the convergence of the stochastic gradient descent for selected formulations even though the gradient estimate is inherently biased. We suggest several numerical improvements, including the implicit derivative and stochastic gradient descent. We provide an extensive numerical study.