Linear Classifiers Under Infinite Imbalance

Paul Glasserman and Mike Li

Papers from arXiv.org

Abstract: We study the behavior of linear discriminant functions for binary classification in the infinite-imbalance limit, where the sample size of one class grows without bound while the sample size of the other remains fixed. The coefficients of the classifier minimize an empirical loss specified through a weight function. We show that for a broad class of weight functions, the intercept diverges but the rest of the coefficient vector has a finite almost sure limit under infinite imbalance, extending prior work on logistic regression. The limit depends on the left-tail growth rate of the weight function, for which we distinguish two cases: subexponential and exponential. The limiting coefficient vectors reflect robustness or conservatism properties in the sense that they optimize against certain worst-case alternatives. In the subexponential case, the limit is equivalent to an implicit choice of upsampling distribution for the minority class. We apply these ideas in a credit risk setting, with particular emphasis on performance in the high-sensitivity and high-specificity regions.

Date: 2021-06, Revised 2023-05
New Economics Papers: this item is included in nep-ecm
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2106.05797 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2106.05797

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().