Related papers: On a prior based on the Wasserstein information ma…

In this paper reference and probability-matching priors are derived for the univariate Student $t$-distribution. These priors generally lead to procedures with properties frequentists can relate to while still retaining Bayes validity. The…

Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue of their being constrained to non-Euclidean spaces like…

We study information matrices for statistical models by the $L^2$-Wasserstein metric. We call them Wasserstein information matrices (WIMs), which are analogs of classical Fisher information matrices. We introduce Wasserstein score functions…

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein information geometry. It defines a parametrization invariant…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

In this paper we leverage on probability over Riemannian manifolds to rethink the interpretation of priors and posteriors in Bayesian inference. The main mindshift is to move away from the idea that "a prior distribution establishes a…

Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework…

We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…

We propose a measure of the impact of any two choices of prior distributions by quantifying the Wasserstein distance between the respective resulting posterior distributions at any fixed sample size. We illustrate this measure on the…

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.

We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…

Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into…

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…