TY - CONF

T1 - Generalization error of invariant classifiers

AU - Sokolić, Jure

AU - Giryes, Raja

AU - Sapiro, Guillermo

AU - Rodrigues, Miguel R.D.

N1 - Publisher Copyright:
Copyright 2017 by the author(s).

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85083937164&partnerID=8YFLogxK

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AN - SCOPUS:85083937164

T2 - 20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017

Y2 - 20 April 2017 through 22 April 2017

ER -