SpheGeoGrad

Compute gradient w.r.t. y of the geodesic distance \(\arccos(x^\top y)\) on a unit hypersphere

Provides implementation of statistical methods for random objects
lying in various metric spaces, which are not necessarily linear spaces.
The core of this package is Fréchet regression for random objects with
Euclidean predictors, which allows one to perform regression analysis
for non-Euclidean responses under some mild conditions.
Examples include distributions in 2-Wasserstein space,
covariance matrices endowed with power metric (with Frobenius metric
as a special case), Cholesky and log-Cholesky metrics, spherical data.
References: Petersen, A., & Müller, H.-G. (2019) <doi:10.1214/17-AOS1624>.

Yaqing Chen

frechet

Statistical Analysis for Random Objects and Non-Euclidean Data

Yidong Zhou

Han Chen

Alvaro Gajardo

Jianing Fan

Qixian Zhong

Paromita Dubey

Kyunghee Han

Satarupa Bhattacharjee

Changbo Zhu

Su I Iao

Poorbita Kundu

Petersen Alexander

Hans-Georg Müller

SpheGeoGrad function

<dl><dt>x, y</dt>
<dd>Two unit vectors.</dd></dl>

Arguments

Compute gradient w.r.t. y of the geodesic distance \(\arccos(x^\top y)\) on a unit hypersphere — SpheGeoGrad

<dl>

<dt>x, y</dt>
<dd>Two unit vectors.</dd>

</dl>

Compute gradient w.r.t. y of the geodesic distance \(\arccos(x^\top y)\) on a unit hypersphere

SpheGeoGrad: Compute gradient w.r.t. y of the geodesic distance \(\arccos(x^\top y)\) on a unit hypersphere

Description

Usage

Value

Arguments