论文标题
测试几何不变性和均衡性
Testing for Geometric Invariance and Equivariance
论文作者
论文摘要
不变且均衡的模型结合了要估计的对象的对称性（此处非参数回归函数$ f：\ MATHCAL {x} \ rightarrow \ Mathbb {r} $）。这些模型的性能更好（相对于$ l^2 $损失），并且越来越多地用于实践中，但是在错误地假定对称性时会遇到问题。在本文中，我们提出了一个用于对任何半集团$ g $的$ g $均衡的测试框架。当对称性不知道先验时，这将使对这种模型的使用有信心。这些测试独立于模型，并且在计算上很快，因此在模型拟合之前可以轻松使用以测试其有效性。
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.
