Related papers: Warped metrics for location-scale models
As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…
Shape spaces are fundamental in a variety of applications including image registration, morphing, matching, interpolation, and shape optimization. In this work, we consider two-dimensional shapes represented by triangular meshes of a given…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
Many phenomena are naturally characterized by measuring continuous transformations such as shape changes in medicine or articulated systems in robotics. Modeling the variability in such datasets requires performing statistics on Lie groups,…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
In this paper, we begin by introducing Clairaut Riemannian warped product maps and establish the condition under which a regular curve becomes a geodesic. We obtain the conditions for a Riemannian warped product map to be Clairaut…
This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…
We discuss a Lie algebraic and differential geometry construction of solutions to some multidimensional nonlinear integrable systems describing diagonal metrics on Riemannian manifolds, in particular those of zero and constant curvature.…
In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the…
We utilize a condition for algebraic curvature operators called surgery stability as suggested by the work of S. Hoelzel to investigate the space of riemannian metrics over closed manifolds satisfying these conditions. Our main result is a…
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the…
In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds $(B,g_B)$ and $(F,g_F)$ furnished with metrics of the form $c^{2}g_B \oplus w^2 g_F$ and, in particular, of the type $w^{2 \mu}g_B \oplus w^2 g_F$,…
Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in a Euclidean space.…
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of…
We propose a new test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representation of these observables are bounded in phase space, and…
The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…