Related papers: Chain-dependent Conditions in Extremal Set Theory

This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…

Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial…

For integers $n\ge s\ge2$, let $e(n,s)$ denote the maximum size of a family $\F\subseteq2^{[n]}$ with no $s$ pairwise disjoint members. The problem of determining $e(n,s)$, now called the Erd\H{o}s--Kleitman problem, is the non-uniform…

The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…

Let $\mathcal G$ be a family of subsets of an $n$-element set. The family $\mathcal G$ is called non-trivial $3$-wise intersecting if the intersection of any three subsets in $\mathcal G$ is non-empty, but the intersection of all subsets is…

We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…

One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization involving only $\forall_n$-formulas for some…

We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…

Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…

We consider a very weak chain condition for a poset, that is the absence of subsets which are order isomorphic to the set of real numbers in their natural ordering; we study generalised radical groups in which this finiteness condition is…

In this article, we introduce the parametric matroid $\ell$-interdiction problem, where $\ell\in\mathbb{N}_{>0}$ is a fixed number of elements allowed to be interdicted. Each element of the matroid's ground set is assigned a weight that…

Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…

Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…

Extreme events are a major concern in statistical modeling. Ran\-dom missing data can constitute a problem when modeling such rare events. Imputation is crucial in these situations and therefore models that describe different imputation…

We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances…

We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…

We investigate the supports of extremal martingale measures with pre-specified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure $Q$ and the denseness in…

We introduce three measures of complexity for families of sets. Each of the three measures, that we call dimensions, is defined in terms of the minimal number of convex subfamilies that are needed for covering the given family: for upper…

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…