Related papers: A proper scoring rule for minimum information copu…
Many statistical studies are concerned with the analysis of observations organized in a matrix form whose elements are count data. When these observations are assumed to follow a Poisson or a multinomial distribution, it is of interest to…
Many two-sample problems call for a comparison of two distributions from an exponential family. Density ratio estimation methods provide ways to solve such problems through direct estimation of the differences in natural parameters. The…
In recent years, probabilistic forecasting is an emerging topic, which is why there is a growing need of suitable methods for the evaluation of multivariate predictions. We analyze the sensitivity of the most common scoring rules,…
It has been argued persuasively that, in order to evaluate climate models, the probability distributions of model output need to be compared to the corresponding empirical distributions of observed data. Distance measures between…
Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…
We derive independence tests by means of dependence measures thresholding in a semiparametric context. Precisely, estimates of phi-mutual informations, associated to phi-divergences between a joint distribution and the product distribution…
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…
Experimental designs are tools which can dramatically reduce the number of simulations required by time-consuming computer codes. Because we don't know the true relation between the response and inputs, designs should allow one to fit a…
This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage…
Copulas are functions that describe dependence structures of random vectors, without describing their univariate marginals. In statistics, the separation is sometimes useful, the quality and/or quantity of available information on these two…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
We study the minimax estimation of $\alpha$-divergences between discrete distributions for integer $\alpha\ge 1$, which include the Kullback--Leibler divergence and the $\chi^2$-divergences as special examples. Dropping the usual…
Experimental designs are tools which can drastically reduce the number of simulations required by time-consuming computer codes. One strategy for selecting the values of the inputs, whose response is to be observed, is to choose these…
Vine pair-copula constructions exist for a mix of continuous and ordinal variables. In some steps, this can involve estimating a bivariate copula for a pair of mixed continuous-ordinal variables. To assess the adequacy of copula fits for…
The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on…
The problem of predicting independent Poisson random variables is commonly encountered in real-life practice. Simultaneous predictive distributions for independent Poisson observables are investigated, and the performance of predictive…
We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
This short note is on a property of the Kullback-Leibler (KL) divergence which indicates that independent Gaussian distributions minimize the KL divergence from given independent Gaussian distributions. The primary purpose of this note is…
In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to…