Related papers: Extremal independence in discrete random systems
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
The behavior of extreme observations is well-understood for time series or spatial data, but little is known if the data generating process is a structural causal model (SCM). We study the behavior of extremes in this model class, both for…
We provide a geometrical characterization of extremal negative dependence as a convex polytope in the simplex of multidimensional Bernoulli distributions, and we prove that it is an antichain that satisfies some minimality conditions with…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
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…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
Extreme events have low occurrence probabilities and display pronounced deviation from their average behaviour, such as earthquakes or power blackouts. Such extreme events occurring on the nodes of a complex network have been extensively…
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…
We consider quadratic forms of deterministic matrices $A$ evaluated at the random eigenvectors of a large $N \times N$ GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
Understanding the spatial extent of extreme precipitation is necessary for determining flood risk and adequately designing infrastructure (e.g., stormwater pipes) to withstand such hazards. While environmental phenomena typically exhibit…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
Let $\mathbf{X}_1,...,\mathbf{X}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1n^{\alpha}\leq p\leq c_2n^{\alpha}$ for some positive constants $c_1,c_2$ and $\alpha$. In this paper we introduce a new…
It is an important fact that extremal discrete structures -- that is, discrete structures of maximal size among those that avoid certain configurations -- exhibit strong pseudorandom behavior. We present instances of this phenomenon in the…
Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (dfs). Dfs are rarely available in…
In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…
We prove new lower bounds on the likely size of a maximum independent set in a random graph with a given average degree. Our method is a weighted version of the second moment method, where we give each independent set a weight based on the…
In this paper we explore maximal deviations of large random structures from their typical behavior. We introduce a model for a high-dimensional random graph process and ask analogous questions to those of Vapnik and Chervonenkis for…