Related papers: Sparsity in Multivariate Extremes with Application…
Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
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…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…
Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…
We propose a spectral clustering algorithm for analyzing the dependence structure of multivariate extremes. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
When modeling a vector of risk variables, extreme scenarios are often of special interest. The peaks-over-thresholds method hinges on the notion that, asymptotically, the excesses over a vector of high thresholds follow a multivariate…
Anomaly detection is a field of intense research. Identifying low probability events in data/images is a challenging problem given the high-dimensionality of the data, especially when no (or little) information about the anomaly is…
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the…
Generating accurate extremes from an observational data set is crucial when seeking to estimate risks associated with the occurrence of future extremes which could be larger than those already observed. Applications range from the…
Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…
Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This…
We present a new framework for modelling multivariate extremes, based on an angular-radial representation of the probability density function. Under this representation, the problem of modelling multivariate extremes is transformed to that…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…