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.
翻译:变量和等式模型包含一个要估计的物体的对称( 在非参数回归函数 $f :\ mathcal{X}\ rightrow \ mathbb{R}$ ) 。 这些模型表现更好( 损失为 $L $2$ ), 在实践中正在越来越多地使用, 但是当对称被错误地假定时遇到了问题 。 在本文中, 我们提出了一个用于测试任何半组 G$ 的对称框架 。 这将在对称未知为先验时对使用这些模型产生信心 。 这些测试独立于模型, 并且计算得很快, 因此在模型安装以测试其有效性之前很容易使用 。