Work

Algebraic analysis of rotation data

Year: 2020

Type: article

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 Gröbner 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.

Source: Algebraic Statistics

DOI: 10.2140/astat.2020.11.189

Authors: Michael F. Adamer, András C. Lőrincz, Anna-Laura Sattelberger, Bernd Sturmfels

Institutions: ETH Zurich, Humboldt-Universität zu Berlin, Max Planck Institute for Mathematics in the Sciences, University of California, Berkeley

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W2990945534

FWCI: 0.354

Cites: 19

Cited by: 3

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