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

Kohler Michael; Krzyzak Adam; Walter Benjamin

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

机译：基于卷积神经网络的图像分类器收敛速率研究

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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.

机译：定义了基于卷积神经网络的图像分类器，分析了估计值的误分类风险向最优误分类风险的收敛率。在对后验概率的平滑度和结构的适当假设下，显示了与图像维度无关的收敛速率。这证明，在图像分类中，通过卷积神经网络规避维数的诅咒是可能的。此外，所获得的结果还说明了为什么卷积神经网络在图像分类中能够优于标准前馈神经网络。我们的分类器使用模拟数据与其他各种分类方法进行比较。此外，我们的估计性能也在真实图像上进行了测试。

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来源
《Annals of the Institute of Statistical Mathematics》 |2022年第6期|1085-1108|共24页
作者
Kohler Michael; Krzyzak Adam; Walter Benjamin;
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作者单位

Tech Univ Darmstadt;

Concordia Univ;

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原文格式 PDF
正文语种英语
中图分类数理统计;
关键词
Curse of dimensionality; Convolutional neural networks; Image classification; Rate of convergence;

机译：维度的诅咒;卷积神经网络;图像分类;收敛速度;

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

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