Invariance to nuisance transformations is one of the desirable properties of
effective representations. We consider transformations that form a \emph{group}
and propose an approach based on kernel methods to derive local group invariant
representations. Locality is achieved by defining a suitable probability
distribution over the group which in turn induces distributions in the input
feature space. We learn a decision function over these distributions by
appealing to the powerful framework of kernel methods and generate local
invariant random feature maps via kernel approximations. We show uniform
convergence bounds for kernel approximation and provide excess risk bounds for
learning with these features. We evaluate our method on three real datasets,
including Rotated MNIST and CIFAR-10, and observe that it outperforms competing
kernel based approaches. The proposed method also outperforms deep CNN on
Rotated-MNIST and performs comparably to the recently proposed
group-equivariant CNN.

本文提出了一种基于核方法的技术来推导局部群不变表示，通过在群上定义适当的概率分布来实现局部性，并使用核方法的强大框架来学习这些分布上的决策函数，从而生成局部不变随机特征映射。经实验证明，在三个真实数据集上，该方法优于基于核的竞争方法，并且在 Rotated-MNIST 上表现优于深度 CNN，并且与最近提出的群等变 CNN 表现相当。