On the rate of convergence of image classifiers based on convolutional neural networks
This provides a theoretical foundation for CNNs in image classification, demonstrating their ability to avoid dimensionality issues, which is crucial for high-dimensional data applications.
The paper analyzes the convergence rate of misclassification risk for convolutional neural network (CNN) image classifiers, showing that under certain smoothness and structural assumptions, the rate is independent of image dimension, thereby circumventing the curse of dimensionality.
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.