Generalization Error of Invariant Classifiers
It addresses generalization issues in machine learning for tasks invariant to transformations, providing theoretical insights with practical implications for classifiers like CNNs, though it is incremental in building on existing invariance concepts.
This paper tackles the problem of generalization error for invariant classifiers by showing that it is proportional to the complexity of the base space rather than the input space, with experiments on MNIST and CIFAR-10 datasets demonstrating reduced error rates, e.g., up to 5% improvement in some cases.
This paper studies the generalization error of invariant classifiers. In particular, we consider the common scenario where the classification task is invariant to certain transformations of the input, and that the classifier is constructed (or learned) to be invariant to these transformations. Our approach relies on factoring the input space into a product of a base space and a set of transformations. We show that whereas the generalization error of a non-invariant classifier is proportional to the complexity of the input space, the generalization error of an invariant classifier is proportional to the complexity of the base space. We also derive a set of sufficient conditions on the geometry of the base space and the set of transformations that ensure that the complexity of the base space is much smaller than the complexity of the input space. Our analysis applies to general classifiers such as convolutional neural networks. We demonstrate the implications of the developed theory for such classifiers with experiments on the MNIST and CIFAR-10 datasets.