Related papers: Gaussian distributions on Riemannian symmetric spa…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
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…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
The importance of wild video based image set recognition is becoming monotonically increasing. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a…
A Stiefel manifold of the compact type is often encountered in many fields of Engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space…
Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…
In this paper we consider the space of those probability distributions which maximize the $q$-R\'enyi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some…
We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables…
The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…
We present a Bayesian model for pairwise nonlinear registration of functional data. We use the Riemannian geometry of the space of warping functions to define appropriate prior distributions and sample from the posterior using importance…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…