We present a method for estimating the maximal symmetry of a continuous 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 generalises useful tools from linear dimension reduction to a non linear context. We show that the estimation is consistent when the subgroup lattice chosen is finite, even when some of the subgroups themselves are infinite. We demonstrate the performance of this estimator in synthetic settings and apply the methods to two data sets: satellite measurements of the earth's magnetic field intensity; and the distribution of sunspots.

翻译：我们提出了一种估计连续回归函数最大对称性的方法。该对称性的知识可以通过消除由对称性引起的变异模态来显著改进建模过程。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。我们证明了唯一最大不变子群G的估计将线性降维中的有用工具推广到了非线性情境。同时证明，当所选的子群格为有限集合时（即使其中某些子群本身是无限的），该估计具有一致性。我们在合成场景中展示了该估计器的性能，并将该方法应用于两个数据集：地球磁场强度的卫星测量数据以及太阳黑子分布数据。