Related papers: Sklar's Theorem in an Imprecise Setting
In this study, we generalize the Fokker-Planck equation to two-dimensional cases, including potential functions with periodic boundary conditions and piecewise-defined structures, to analyze the probability distribution in multi-field…
In probabilistic modelling, joint distributions are often of more interest than their marginals, but the standard composition of stochastic channels is defined by marginalization. Last year at ACT, the notion of 'copy-composition' was…
We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals,…
Nonparanormal models describe the joint distribution of multivariate responses via latent Gaussian, and thus parametric, copulae while allowing flexible nonparametric marginals. Some aspects of such distributions, for example conditional…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
Proximity Distribution Kernel is an effective method for bag-of-featues based image representation. In this paper, we investigate the soft assignment of visual words to image features for proximity distribution. Visual word contribution…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
We introduce from an analytic perspective Christoffel-Darboux kernels associated to bounded, tracial noncommutative distributions. We show that properly normalized traces, respectively norms, of evaluations of such kernels on finite…
The Schr\"oder-Bernstein theorem states that, for any two sets P and Q, if there exists an injection from P to Q and an injection from Q to P, then there must exist a bijection between the two sets. Classically, it follows that the ordering…
In spite of recent contributions to the literature, informative cluster size settings are not well known and understood. In this paper, we give a formal definition of the problem and describe it from different viewpoints. Data generating…
As a motivating problem, we aim to study some special aspects of the marginal distributions of the order statistics for exchangeable and (more generally) for minimally stable non-negative random variables $T_{1},...,T_{r}$. In any case, we…
Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal…
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups.…
Conditional copulas are flexible statistical tools that couple joint conditional and marginal conditional distributions. In a linear regression setting with more than one covariate and two dependent outcomes, we propose the use of additive…