Related papers: Characterization of multivariate Bernoulli distrib…
Let $\mu$ be a probability distribution on $\mathbb{R}^d$ which assigns measure zero to every hyperplane and $S$ a set of points sampled independently from $\mu$. What can be said about the expected combinatorial structure of the convex…
Let $B_p^n$ be the unit ball of $\ell_p^n$, with $1\le p<2$. We study central densities of one-dimensional marginals of the uniform measure on $B_p^n$ and of its Gaussian heat-flow regularizations. The profile is standardized by multiplying…
The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation…
Copulas are a powerful tool to model dependence between the components of a random vector. One well-known class of copulas when working in two dimensions is the Farlie-GumbelMorgenstern (FGM) copula since their simple analytic shape enables…
In this note we investigate the convex hull of those $n \times n$-permutation matrices that correspond to symmetries of a regular $n$-gon. We give the complete facet description. As an application, we show that this yields a Gorenstein…
It is well known that the convex hull of $\{(x,y,xy)\}$, where $(x,y)$ is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti {\em et al.\,}(2010) and Miller {\em et al.\,}(2011)…
In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of…
We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…
In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type $W=X_1/(X_1+X_2)$, where $(X_1, X_2)^\top$ follows a bivariate extreme distribution with Fr\'echet margins, that is, $X_1$…
The notion of margin loss has been central to the development and analysis of algorithms for binary classification. To date, however, there remains no consensus as to the analogue of the margin loss for multiclass classification. In this…
We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution,…
We derive a partition function for the Lund fragmentation model and compare it with that of a classical gas. For a fixed rapidity ``volume'' this partition function corresponds to a multiplicity distribution which is very close to a…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…
Level curvature is a measure of sensitivity of energy levels of a disordered/chaotic system to perturbations. In the bulk of the spectrum Random Matrix Theory predicts the probability distributions of level curvatures to be given by…
In this article we define new Fr\`Echet features for random cumulative distribution functions using contrast. These contrasts allow to construct Wasserstein costs and our new features minimize the average costs as the Fr\`Echet mean…
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, Choquet decompositions and Choquet convex decompositions, as well as their corresponding hull operators…
A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was…