Related papers: Geomstats: A Python Package for Riemannian Geometr…

Since Lorenz's seminal work on a simplified weather model, the numerical analysis of nonlinear dynamical systems has become one of the main subjects of research in physics. Despite of that, there remains a need for accessible, efficient,…

Riemannian geometry is a mathematical field which has been the cornerstone of revolutionary scientific discoveries such as the theory of general relativity. Despite early uses in robot design and recent applications for exploiting data with…

This paper describes open-source scientific contributions in python surrounding the numerical solutions to hyperbolic Hamilton-Jacobi (HJ) partial differential equations viz., their implicit representation on co-dimension one surfaces;…

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…

Riemannian manifolds provide a principled way to model nonlinear geometric structure inherent in data. A Riemannian metric on said manifolds determines geometry-aware shortest paths and provides the means to define statistical models…

\texttt{Mixture-Models} is an open-source Python library for fitting Gaussian Mixture Models (GMM) and their variants, such as Parsimonious GMMs, Mixture of Factor Analyzers, MClust models, Mixture of Student's t distributions, etc. It…

We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the exponential parameter space of product manifolds of categorical distributions as a novel method…

We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a…

For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns, while…

PyGALAX is a Python package for geospatial analysis that integrates automated machine learning (AutoML) and explainable artificial intelligence (XAI) techniques to analyze spatial heterogeneity in both regression and classification tasks.…

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…

Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance…

The indicator matrix plays an important role in machine learning, but optimizing it is an NP-hard problem. We propose a new relaxation of the indicator matrix and prove that this relaxation forms a manifold, which we call the Relaxed…

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…

We study geodesics of the form $\gamma(t)=\pi(\exp(tX)\exp(tY))$, $X,Y\in \fr{g}=\operatorname{Lie}(G)$, in homogeneous spaces $G/K$, where $\pi:G\rightarrow G/K$ is the natural projection. These curves naturally generalise homogeneous…

`scores` is a Python package containing mathematical functions for the verification, evaluation and optimisation of forecasts, predictions or models. It supports labelled n-dimensional (multidimensional) data, which is used in many…

Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in…

Machine learning techniques offer a precious tool box for use within astronomy to solve problems involving so-called big data. They provide a means to make accurate predictions about a particular system without prior knowledge of the…

Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational…