General framework for binary classification on top samples

0551866 - ÚTIA 2023 RIV GB eng J - Journal Article
Adam, L. - Mácha, V. - Šmídl, Václav - Pevný, T.
General framework for binary classification on top samples.
Optimization Methods & Software. Roč. 37, č. 5 (2022), s. 1636-1667. ISSN 1055-6788. E-ISSN 1029-4937
R&D Projects: GA ČR GA18-21409S
Institutional support: RVO:67985556
Keywords : general framework * classification * ranking * accuracy at the top * Neyman–Pearson * Pat&Mat
OECD category: Applied mathematics
Impact factor: 2.2, year: 2022
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2022/AS/smidl-0551866.pdf https://www.tandfonline.com/doi/full/10.1080/10556788.2021.1965601

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.
Permanent Link: https://hdl.handle.net/11104/0337818