arXiv research

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

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.

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.

Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet sim…

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.

A $q$-Gaussian measure is a generalization of a Gaussian measure. This generalization is obtained by replacing the exponential function with the power function of exponent $1/(1-q)$ ($q\neq 1$). The limit case $q=1$ recovers a Gaussian measure. For $1\leq q <3$, the set of all $q$-Gaussian densities over the real line …

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

Extends Gaussian process theory to Banach spaces.

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

New method for spatiotemporal data regression using Gaussian processes.

Kernel embeddings separate distinct probability distributions, simplifying testing.

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…

Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various multivariate risk measures significantly. In this contribution we derive precise approxim…

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

Paper extends FOFC algorithm to work with mixed data types.

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

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

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

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.

It is shown that $m$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with minimum Gaussian surface area must be $(m-1)$-dimensional. This follows from a second variation argument using infinitesimal translations. The special case $m=3$ proves the Double Bubble problem for the Gaussian measure,…

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

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 $M$.

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…

The paper extends inequalities for projection bodies to arbitrary measures.

Paper calculates KL divergence for isotropic Gaussian-Markov fields.

Bayesian framework predicts aerodynamic uncertainty from sparse measurements.

A novel kernel-based test detects equality versus singularity of two probability measures.

Proposes a robust similarity measure for sparse time series data.

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apoll…

Fisher width is a geometric measure of complexity on statistical manifolds.

We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing it. The resulting measure is shown to satisfy a number of desirable properties. …

We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mi…

Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to …