arXiv research

Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.

Proposes Gaussian Processes for more accurate time-correlated measurement noise in robotics.

Study approximates multivariate risk measures for Gaussian risks.

Solves $L_p$-Gaussian chord Minkowski problem using Gauss curvature flow.

Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.

The space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By restricting to the space of Gaussian measures inside the $L^2$-Wasserstein space, we manag…

Study entropic regularization of Gaussian measures and processes on Hilbert space.

Researchers explore gauge freedom in entropies of $q$-Gaussian measures.

New multivariate dependency measure using Gaussian kernel and copula.

Study on conditioning Gaussian measures on nonlinear observations, including representer theorem and mode estimation.

Study non-Gaussian measures' concentration properties in metric spaces.

Paper presents characteristic function of Tsallis q-Gaussian and its applications.

Method identifies low-dimensional structure in high-dimensional probability measures.

This study describes the Fisher-Rao metric on Gaussian measures in infinite-dimensional spaces.

FPI methods compute barycenters of Gaussian sets for various dissimilarity measures.

Minimal Gaussian surfaces partitioning space with minimum area.

Proposes Gaussian optimal transport for image style transfer.

Study predicts Gaussian Volterra processes with noisy Brownian motion.

The paper proposes a new framework for accurate uncertainty representation and propagation.

The paper analyzes Laplace learning for Gaussian measure data in infinite dimensions, proving convergence.

Extends Gaussian process theory to Banach spaces.

Researchers prove the least perimeter way to divide space into three parts.

Kernel embeddings separate distinct probability distributions, simplifying testing.

New method for spatiotemporal data regression using Gaussian processes.

Paper introduces a new distance measure for Gaussian Mixture Models.

The study analyzes the evolution of Gaussian measures under a specific gradient flow.

This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the regular Gaussian distributions that factorize with respect to a chain graph $G$ with $d$ parameters have positive Lebesgue measure with respect to $\mathbb{R}^d$, whereas those that factorize with respect…

The paper associates path measures to surface curvature.

This work studies Gaussian geometry under entropy-regularized 2-Wasserstein distance.

Paper extends FOFC algorithm to work with mixed data types.

The study examines the behavior of Gaussian processes' minimums and overshoots.

New KL-divergence for Gaussian distributions based on Wasserstein geometry.

New method detects causal relationships from noisy measurements.

Novel method uses Gaussian process to estimate particle sizes from scattering data.

This paper addresses Gaussian Process regression over probability measures, revealing a non-stationarity issue between Euclidean and Wasserstein kernels.

This work extends entropic optimal transport to non-product reference couplings, focusing on Gaussian cases.

Optimizes parameter reconstruction for optical scatterometry using Gaussian process regression.

This work proposes new methods for variational inference using gradient flows on Gaussian measures.

Deep kernel learning for complex function modeling.

A new method optimizes robustness measures under input uncertainty using randomized Gaussian process upper confidence bound.

DKF uses nonlinear, Gaussian approximations for better neural decoding.

Agents learn state ambiguity from non-linear sensor data using Gaussian approximations.

Many sensors, such as range, sonar, radar, GPS and visual devices, produce measurements which are contaminated by outliers. This problem can be addressed by using fat-tailed sensor models, which account for the possibility of outliers. Unfortunately, all estimation algorithms belonging to the family of Gaussian filters…

Quantum neural networks converge to Gaussian processes as they grow.

Proves least Gaussian perimeter decomposition conjectures for 2-3 cells in n-dimensional space.

Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.

We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e.g., a standard Gaussian) with a tar…

We prove that the ring $\Aff{\R}{M}$ of all polynomials defined on a real algebraic variety $M\subset\R^n$ is dense in the Hilbert space $L^2(M,e^{-|x|^2}\deμ)$, where $\deμ$ denotes the volume form of $M$ and $\deν=e^{-|x|^2}\deμ$ the Gaussian measure on $M$.