Related papers: A Natural Copula
In this article, we represent the Wasserstein metric of order $p$, where $p\in [1,\infty)$, in terms of the comonotonicity copula, for the case of probability measures on $\R^d$, by revisiting existing results. In 1973, Vallender…
Finding upper and lower bounds to integrals with respect to copulas is a quite prominent problem in applied probability. In their 2014 paper, Hofer and Iaco showed how particular two dimensional copulas are related to optimal solutions of…
Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the…
Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
We generalize 2-Wasserstein dependence coefficients to measure dependence between a finite number of random vectors. This generalization includes theoretical properties, and in particular focuses on an interpretation of maximal dependence…
The concept of asymmetric copulas is revisited and is made more precise. We give a rigorous topological argument for opportunity to define asymmetry measures defined recently by K.F Siburg [6] through exhibiting at least three ordered…
This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of…
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…
Linear fluctuating hydrodynamics is a useful and versatile tool for describing fluids, as well as other systems with conserved fields, on a mesoscopic scale. In one spatial dimension, however, transport is anomalous, which requires to…
We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.
A Copula density estimation method that is based on a finite mixture of heterogeneous parametric copula densities is proposed here. More specifically, the mixture components are Clayton, Frank, Gumbel, T, and normal copula densities, which…
Estimation of mutual information between random variables has become crucial in a range of fields, from physics to neuroscience to finance. Estimating information accurately over a wide range of conditions relies on the development of…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
A bivariate distribution with continuous margins can be uniquely decomposed via a copula and its marginal distributions. We consider the problem of estimating the copula function and adopt a Bayesian approach. On the space of copula…
The application of the Cauchy distribution has often been discussed as a potential model of the financial markets. In particular the way in which single extreme, or "Black Swan", events can impact long term historical moments, is often…
Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged…
We introduce novel belief propagation algorithms to estimate the marginals of a high dimensional probability distribution. They involve natural (co)homological constructions relevant for a localised description of statistical systems.
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference…
Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…