The use of personal data for training machine learning systems comes with a privacy threat and measuring the level of privacy of a model is one of the major challenges in machine learning today. Identifying training data based on a trained model is a standard way of measuring the privacy risks induced by the model. We develop a novel approach to address the problem of membership inference in pattern recognition models, relying on information provided by adversarial examples. The strategy we propose consists of measuring the magnitude of a perturbation necessary to build an adversarial example. Indeed, we argue that this quantity reflects the likelihood of belonging to the training data. Extensive numerical experiments on multivariate data and an array of state-of-the-art target models show that our method performs comparable or even outperforms state-of-the-art strategies, but without requiring any additional training samples.

Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common characterization of extremes’ dependence structure is the angular measure. It is a suitable measure to work in extreme regions as it provides meaningful insights concerning the subregions where extremes tend to concentrate their mass. The present paper develops a novel optimization-based approach to assess the dependence structure of extremes. This support identification scheme rewrites as estimating clusters of features which best capture the support of extremes. The dimension reduction technique we provide is applied to statistical learning tasks such as feature clustering and anomaly detection. Numerical experiments provide strong empirical evidence of the relevance of our approach.

The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method to learn a heavy-tailed embedding with desirable regularity properties regarding the distributional tails, which allows to analyze the points far away from the distribution bulk using the framework of multivariate extreme value theory. In particular, a classifier dedicated to the tails of the proposed embedding is obtained which exhibits a scale invariance property exploited in a novel text generation method for label preserving dataset augmentation. Experiments on synthetic and real text data show the relevance of the proposed framework and confirm that this method generates meaningful sentences with controllable attribute, e.g. positive or negative sentiments.

In pattern recognition, a random label Y is to be predicted based upon observing a random vector X valued in $\mathbb{R}^d$ 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.