Title: On binary classification in extreme regions
Authors: Anne Sabourin - Telecom Paris, Institut Polytechnique de Paris (France) [presenting]
Stephan Clemencon - Telecom ParisTech (France)
Hamid Jalalzai - Telecom ParisTech (France)
Abstract: In pattern recognition, a random label $Y$ is to be predicted based upon observing a random vector $X$ valued in $R^d$ with $d\geq 1$ by means of a classification rule with minimum probability of error. In a wide variety of applications, extreme 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. The aim is to develop a general framework for classification of extreme data. Precisely, under heavy-tail assumptions for the class distributions, we introduce a natural and asymptotic notion of risk, accounting for predictive performance in extreme regions of the input space. We 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.