On Binary Classification in Extreme Regions - IMT - Institut Mines-Télécom Access content directly
Proceedings Year : 2018

On Binary Classification in Extreme Regions


In pattern recognition, a random label Y is to be predicted based upon observing a random vector X valued in R d with d ≥ 1 by means of a classification rule with minimum probability of error. In a wide variety of applications, ranging from finance/insurance to environmental sciences through teletraffic data analysis for instance, extreme (i.e. very large) observations X are of crucial importance, while contributing in a negligible manner to the (empirical) error however, simply because of their rarity. As a consequence, empirical risk minimizers generally perform very poorly in extreme regions. It is the purpose of this paper to develop a general framework for classification in the extremes. Precisely, under non-parametric heavy-tail assumptions for the class distributions, we prove that a natural and asymptotic notion of risk, accounting for predictive performance in extreme regions of the input space, can be defined and show that minimizers of an empirical version of a non-asymptotic approximant of this dedicated risk, based on a fraction of the largest observations, lead to classification rules with good generalization capacity, by means of maximal deviation inequalities in low probability regions. Beyond theoretical results, numerical experiments are presented in order to illustrate the relevance of the approach developed
Fichier principal
Vignette du fichier
inproceedings-2018-18398-4.pdf (778.84 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01932813 , version 1 (23-11-2018)


  • HAL Id : hal-01932813 , version 1


Hamid Jalalzai, Stéphan Clémençon, Anne Sabourin. On Binary Classification in Extreme Regions. 2018. ⟨hal-01932813⟩
213 View
177 Download


Gmail Facebook X LinkedIn More