Work

Estimating maximal symmetries of regression functions via subgroup lattices

Year: 2025

Type: article

Abstract: We present a method for estimating the maximal symmetry of a continuous regression function. Knowledge of such a symmetry can be used to significantly improve modelling by removing the modes of variation resulting from the symmetries. Symmetry estimation is carried out using hypothesis testing for invariance strategically over the subgroup lattice of a search group G acting on the feature space. We show that the estimation of the unique largest invariant subgroup of G generalizes useful tools from linear dimension reduction to a non-linear context. We show that the estimation is consistent when the subgroup lattice chosen is finite, even when some of the subgroups themselves are infinite. We demonstrate the performance of this estimator in synthetic settings and apply the methods to 2 data sets: satellite measurements of the Earth’s magnetic field intensity and the distribution of sunspots.

Source: Apollo (University of Cambridge)

DOI: 10.17863/cam.118441

Authors: Christie, Louis G, Aston, John AD

Language: English

Topic: Statistical Methods and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: Real-time digital optimisation and decision making for energy and transport systems

OpenAlex ID: W6906581089

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