DeepAI AI Chat
Log In Sign Up

Algebraic Analysis of Rotation Data

by   Michael F Adamer, et al.
Max Planck Society

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.


page 1

page 2

page 3

page 4


Computing representation matrices for the action of Frobenius to cohomology groups

This paper is concerned with the computation of representation matrices ...

Kernel Stein Discrepancy on Lie Groups: Theory and Applications

Distributional approximation is a fundamental problem in machine learnin...

Discussion of "Vintage factor analysis with Varimax performs statistical inference"

We wholeheartedly congratulate Drs. Rohe and Zeng for their insightful p...

Maximum likelihood estimation of the Fisher-Bingham distribution via efficient calculation of its normalizing constant

This paper proposes an efficient numerical integration formula to comput...

Rotation to Sparse Loadings using L^p Losses and Related Inference Problems

Exploratory factor analysis (EFA) has been widely used to learn the late...

Formalising Fisher's Inequality: Formal Linear Algebraic Proof Techniques in Combinatorics

The formalisation of mathematics is continuing rapidly, however combinat...

u-generation: solving systems of polynomials equation-by-equation

We develop a new method that improves the efficiency of equation-by-equa...