We present a method for estimating the maximal symmetry of a regression function. Knowledge of such a symmetry can be used to significantly improve modelling by removing the modes of variation resulting from the symmetries. Symmetry estimation is carried out using hypothesis testing for invariance strategically over the subgroup lattice of a search group G acting on the feature space. We show that the estimation of the unique maximal invariant subgroup of G can be achieved by testing on only a finite portion of the subgroup lattice when G_max is a compact subgroup of G, even for infinite search groups and lattices (such as for the 3D rotation group SO(3)). We then show that the estimation is consistent when G is finite. We demonstrate the performance of this estimator in low dimensional simulations, on a synthetic image classification on MNIST data, and apply the methods to an application using satellite measurements of the earth's magnetic field.

翻译：我们提出了一种估计回归函数最大对称性的方法。此类对称性的知识可通过消除由对称性引起的变异模式，显著改进建模。对称性估计通过策略性地在作用于特征空间的搜索群G的子群格上进行不变性假设检验来实现。我们证明，当G_max是G的紧子群时，即使对无限搜索群和子群格（例如三维旋转群SO(3)），仅需对子群格的有限部分进行检验即可实现对G的唯一最大不变子群的估计。随后我们证明，当G为有限群时，该估计具有一致性。我们在低维模拟、基于MNIST数据的合成图像分类中展示了该估计器的性能，并将该方法应用于地球磁场卫星测量数据的实际场景。