Testing for Geometric Invariance and Equivariance
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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 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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