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

2020/03/03 by M. Kohler, A. Krzyzak, Kohler, M. +3 · 1 citation
Computer Science · #Advanced Computational Techniques in Science and Engineering #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · pdf · doi:10.48550/arxiv.2003.01526

openalex publication_date 2020/03/03 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

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 the aposteriori probability a 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.

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