相关论文: Polynomial Regression on Riemannian Manifolds

Building on Dryden et al. (2021), this note presents the Bayesian estimation of a regression model for size-and-shape response variables with Gaussian landmarks. Our proposal fits into the framework of Bayesian latent variable models and…

We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. Recently, we have shown that in four dimensions a Lorentzian spacetime…

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds which are not modeled on Banach spaces. The present article…

We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…

We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…

On an odd-dimensional oriented hyperbolic manifold of finite volume with strongly acyclic coefficient systems, we derive a formula relating analytic torsion with the Reidemeister torsion of the Borel-Serre compactification of the manifold.…

In this study, a density-on-density regression model is introduced, where the association between densities is elucidated via a warping function. The proposed model has the advantage of a being straightforward demonstration of how one…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

We study the singular cohomology of the moduli space of rank 2 parabolic bundles on a Riemann surface where the weights are all 1/4. We give a formula, based on work of Boden, for the Poincar\'e polynomial of this moduli space in general,…

This paper introduces a novel approach to statistics and data analysis, departing from the conventional assumption of data residing in Euclidean space to consider a Riemannian Manifold. The challenge lies in the absence of vector space…

In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…

In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…

Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…

We investigate combining imaging and shape features extracted from MRI for the clinically relevant tasks of brain age prediction and Alzheimer's disease classification. Our proposed model fuses ResNet-extracted image embeddings with shape…

This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel…

In this study, we proposed and evaluated a graph-based framework to assess variations in Alzheimer's disease (AD) neuropathologies, focusing on classic (cAD) and rapid (rpAD) progression forms. Histopathological images are converted into…

This paper deals with the computation of sectional curvature for the manifolds of $N$ landmarks (or feature points) in D dimensions, endowed with the Riemannian metric induced by the group action of diffeomorphisms. The inverse of the…

Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective.…

Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label $y\in {\cal R}$ as a…