Related papers: Fisher-Rao distance and pullback SPD cone distance…

The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…

This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian…

This paper explores a novel connection between two areas: shape analysis of surfaces and unbalanced optimal transport. Specifically, we characterize the square root normal field (SRNF) shape distance as the pullback of the…

The space of all probability measures having positive density function on a connected compact smooth manifold $M$, denoted by $\mathcal{P}(M)$, carries the Fisher information metric $G$. We define the geometric mean of probability measures…

Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…

Resource-efficiently computing representations of probability distributions and the distances between them while only having access to the samples is a fundamental and useful problem across mathematical sciences. In this paper, we propose a…

The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…

In this work, we perform an in-depth study of recently introduced average-case quantum distances. The average-case distances approximate the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in…

The high-dimensional parameter space of deep neural networks -- the neuromanifold -- is endowed with a unique metric tensor defined by the Fisher information. Reliable and scalable computation of this metric tensor is valuable for theorists…

The learning of Gaussian Mixture Models (also referred to simply as GMMs) plays an important role in machine learning. Known for their expressiveness and interpretability, Gaussian mixture models have a wide range of applications, from…

The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric…

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…

Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more…

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…

This paper deals with Cram\'er-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces generalized versions of Fisher…

The Fisher-Bingham distribution ($\mathrm{FB}_8$) is an eight-parameter family of probability density functions (PDF) on $S^2$ that, under certain conditions, reduce to spherical analogues of bivariate normal PDFs. Due to difficulties in…

We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…

The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian manifolds and generalizes the notion of hyperplanes. As several…

Fairness concerns are increasingly critical as machine learning models are deployed in high-stakes applications. While existing fairness-aware methods typically intervene at the model level, they often suffer from high computational costs,…