Related papers: Geomstats: A Python Package for Riemannian Geometr…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
\texttt{GooStats} is a software framework that provides a flexible environment and common tools to implement multi-variate statistical analysis. The framework is built upon the \texttt{CERN ROOT}, \texttt{MINUIT} and \texttt{GooFit}…
Meta-analysis methods are used to combine evidence from multiple studies. Meta-regression as well as model-based meta-analysis are extensions of standard pairwise meta-analysis in which information about study-level covariates and…
The exponential growth of complex data demands fully automatic clustering. Gaussian mixture models (GMMs) provide uncertainty-aware grouping but often require expertise to specify hyperparameters, e.g., component count and covariance…
Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…
The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…
In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
Recent breakthroughs and rapid integration of generative models (GMs) have sparked interest in the problem of model attribution and their fingerprints. For instance, service providers need reliable methods of authenticating their models to…
We introduce PyChEst, a Python package which provides tools for the simultaneous estimation of multiple changepoints in the distribution of piece-wise stationary time series. The nonparametric algorithms implemented are provably consistent…
There is a need for open-source libraries in emission tomography that (i) use modern and popular backend code to encourage community contributions and (ii) offer support for the multitude of reconstruction techniques available in recent…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of…
Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…
Shape-constrained nonparametric regression is a growing area in econometrics, statistics, operations research, machine learning and related fields. In the field of productivity and efficiency analysis, recent developments in the…
We introduce geoplotlib, an open-source python toolbox for visualizing geographical data. geoplotlib supports the development of hardware-accelerated interactive visualizations in pure python, and provides implementations of dot maps,…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning,…
Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…