Related papers: Gaussian distributions on Riemannian symmetric spa…

The geometric mean is shown to be an appropriate statistic for the scale of a heavy-tailed coupled Gaussian distribution or equivalently the Student's t distribution. The coupled Gaussian is a member of a family of distributions…

We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions. This structure arises in several optimization problems in statistics and machine learning, e.g., for matrix scaling,…

The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…

Bayesian methods constitute a popular approach for estimating the conditional independence structure in Gaussian graphical models, since they can quantify the uncertainty through the posterior distribution. Inference in this framework is…

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…

We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta,…

Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

When characterizing materials, it can be important to not only predict their mechanical properties, but also to estimate the probability distribution of these properties across a set of samples. Constitutive neural networks allow for the…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

We present a method for estimating conditionally Gaussian random vectors with random covariance matrices, which uses techniques from the field of machine learning. Such models are typical in communication systems, where the covariance…

Partitioning a set of elements into subsets of a priori unknown sizes is essential in many applications. These subset sizes are rarely explicitly learned - be it the cluster sizes in clustering applications or the number of shared versus…

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…

Reparameterizable densities are an important way to learn probability distributions in a deep learning setting. For many distributions it is possible to create low-variance gradient estimators by utilizing a `reparameterization trick'. Due…

In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…

We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…

In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…

We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly\,log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample…