Related papers: Deterministic Sampling of Multivariate Densities b…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are…

Phenomena such as air pollution levels are of greatest interest when observations are large, but standard prediction methods are not specifically designed for large observations. We propose a method, rooted in extreme value theory, which…

Collaborative filtering, a widely-used recommendation technique, predicts a user's preference by aggregating the ratings from similar users. As a result, these measures cannot fully utilize the rating information and are not suitable for…

Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically…

The goal of probabilistic prediction is to issue predictive distributions that are as informative as possible, subject to being calibrated. Despite substantial progress in the univariate setting, achieving multivariate calibration remains…

Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…

The Radon cumulative distribution transform (R-CDT), is an easy-to-compute feature extractor that facilitates image classification tasks especially in the small data regime. It is closely related to the sliced Wasserstein distance and…

This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…

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…

This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…

Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…

The shrinking rank method is a variation of slice sampling that is efficient at sampling from multivariate distributions with highly correlated parameters. It requires that the gradient of the log-density be computable. At each individual…

In this report, the explicit probability density functions of the random Euclidean distances associated with equilateral triangles are given, when the two endpoints of a link are randomly distributed in 1) the same triangle, 2) two adjacent…

Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the…

Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…