Algebraic Analysis of Rotation Data
Statistics Theory
2020-12-30 v1 Symbolic Computation
Algebraic Geometry
Optimization and Control
Statistics Theory
Abstract
We develop algebraic tools for statistical inference from samples of rotation matrices. This rests on the theory of D-modules in algebraic analysis. Noncommutative Gr\"obner bases are used to design numerical algorithms for maximum likelihood estimation, building on the holonomic gradient method of Sei, Shibata, Takemura, Ohara, and Takayama. We study the Fisher model for sampling from rotation matrices, and we apply our algorithms for data from the applied sciences. On the theoretical side, we generalize the underlying equivariant D-modules from SO(3) to arbitrary Lie groups. For compact groups, our D-ideals encode the normalizing constant of the Fisher model.
Cite
@article{arxiv.1912.00396,
title = {Algebraic Analysis of Rotation Data},
author = {Michael F. Adamer and András C. Lőrincz and Anna-Laura Sattelberger and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1912.00396},
year = {2020}
}
Comments
21 pages