Estimating maximal symmetries of regression functions via subgroup lattices
提出一种估计连续回归函数最大对称性的方法，通过假设检验在特征空间作用群G的子群格上寻找最大不变子群，将线性降维推广到非线性场景，并在合成数据和两个真实数据集上验证了性能。
Abstract 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 largest invariant subgroup of G generalizes 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 2 data sets: satellite measurements of the Earth’s magnetic field intensity and the distribution of sunspots.