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preprint · arXiv (Cornell University) · 2016

Generalization Error of Invariant Classifiers

Jure Sokolić, Raja Giryes, Guillermo Sapiro, Miguel R. D. Rodrigues

Cited by 19Open access

Abstract

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.

Cite this paper

APA 7

Sokolić, J., Giryes, R., Sapiro, G., & Rodrigues, M. R. D. (2016). Generalization Error of Invariant Classifiers. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1610.04574

MLA 9

Sokolić, Jure, et al. “Generalization Error of Invariant Classifiers.” arXiv (Cornell University), 2016, https://doi.org/10.48550/arxiv.1610.04574.

Chicago

Sokolić, Jure, Raja Giryes, Guillermo Sapiro, and Miguel R. D. Rodrigues. 2016. “Generalization Error of Invariant Classifiers.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1610.04574.

Harvard

Sokolić, J. et al. (2016) ‘Generalization Error of Invariant Classifiers’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1610.04574.

BibTeX
@misc{sokolic2016generalization,
  title = {{Generalization Error of Invariant Classifiers}},
  author = {Sokolić, Jure and Giryes, Raja and Sapiro, Guillermo and Rodrigues, Miguel R. D.},
  journal = {arXiv (Cornell University)},
  year = {2016},
  doi = {10.48550/arxiv.1610.04574}
}

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