Testing for Geometric Invariance and Equivariance

• URL: http://arxiv.org/abs/2205.15280v1
• Date: Mon, 30 May 2022 17:43:18 GMT
• Title: Testing for Geometric Invariance and Equivariance
• Authors: Louis G. Christie and John A. D. Aston
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Invariant and equivariant models incorporate the symmetry of an object to be estimated (here non-parametric regression functions $f : \mathcal{X} \rightarrow \mathbb{R}$). These models perform better (with respect to $L^2$ 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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