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Found 9 papers, 4 papers with code
Geomstats: A Python Package for Riemannian Geometry in Machine Learning
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more.
Learning Weighted Submanifolds with Variational Autoencoders and Riemannian Variational Autoencoders
One of the challenges that naturally arises consists of finding a lower-dimensional subspace for representing such manifold-valued data.
Estimation of Orientation and Camera Parameters from Cryo-Electron Microscopy Images with Variational Autoencoders and Generative Adversarial Networks
As such, it opens the door to geometric approaches for unsupervised estimations of orientations and camera parameters, making possible fast cryo-EM biomolecule reconstruction.
Convex Hierarchical Clustering for Graph-Structured Data
Convex clustering is a recent stable alternative to hierarchical clustering.
Uncertainty Quantification in Multivariate Mixed Models for Mass Cytometry Data
In this article, our aim is to exhibit the use of statistical analyses on the raw, uncompressed data thus improving replicability, and exposing multivariate patterns and their associated uncertainty profiles.
Applications
Template shape estimation: correcting an asymptotic bias
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape.
Positive Curvature and Hamiltonian Monte Carlo
The Jacobi metric introduced in mathematical physics can be used to analyze Hamiltonian Monte Carlo (HMC).
Curvature and Concentration of Hamiltonian Monte Carlo in High Dimensions
In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable Riemannian manifold.
Probability Differential Geometry Statistics Theory Statistics Theory
Waste Not, Want Not: Why Rarefying Microbiome Data is Inadmissible
We use statistical theory, extensive simulations, and empirical data to show that variance stabilizing normalization using a mixture model like the negative binomial is appropriate for microbiome count data.
