Local Group Invariant Representations via Orbit Embeddings
This work addresses the need for robust feature representations in machine learning that are invariant to nuisance transformations, offering a novel kernel-based solution with competitive results, though it is incremental relative to existing group-invariant methods.
The paper tackles the problem of learning representations invariant to group transformations by proposing a kernel-based method that uses local group invariant representations via orbit embeddings, achieving performance improvements on datasets like Rotated MNIST and CIFAR-10, where it outperforms competing kernel approaches and matches group-equivariant CNNs.
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.