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

被引:9
作者
Kohler, Michael [1 ]
Krzyzak, Adam [2 ]
Walter, Benjamin [1 ]
机构
[1] Tech Univ Darmstadt, Fachbereich Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany
[2] Concordia Univ, Dept Comp Sci & Software Engn, 1455 Maisonneuve Blvd West, Montreal, PQ H3G 1M8, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Curse of dimensionality; Convolutional neural networks; Image classification; Rate of convergence;
D O I
10.1007/s10463-022-00828-4
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:1085 / 1108
页数:24
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