Testing for Geometric Invariance and Equivariance

2022/05/30 by Christie, Louis G., Aston, John A. D.
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2205.15280

Abstract

Invariant and equivariant models incorporate the symmetry of an object to be estimated (here non-parametric regression functions f : X → ℝ). These models perform better (with respect to L² loss) and are increasingly being used in practice, but encounter problems when the symmetry is falsely assumed. In this paper we present a framework for testing for G-equivariance for any semi-group G. This will give confidence to the use of such models when the symmetry is not known a priori. These tests are independent of the model and are computationally quick, so can be easily used before model fitting to test their validity.

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