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On the rate of convergence of image classifiers based on convolutional neural networks

Author

Listed:
  • Michael Kohler

    (Technische Universität Darmstadt)

  • Adam Krzyżak

    (Concordia University)

  • Benjamin Walter

    (Technische Universität Darmstadt)

Abstract

Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Under suitable assumptions on the smoothness and structure of a posteriori probability, the rate of convergence is shown which is independent of the dimension of the image. This proves that in image classification, it is possible to circumvent the curse of dimensionality by convolutional neural networks. Furthermore, the obtained result gives an indication why convolutional neural networks are able to outperform the standard feedforward neural networks in image classification. Our classifiers are compared with various other classification methods using simulated data. Furthermore, the performance of our estimates is also tested on real images.

Suggested Citation

  • Michael Kohler & Adam Krzyżak & Benjamin Walter, 2022. "On the rate of convergence of image classifiers based on convolutional neural networks," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1085-1108, December.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:6:d:10.1007_s10463-022-00828-4
    DOI: 10.1007/s10463-022-00828-4
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