Rate of convergence of image classifiers based on convolutional neural network

• Applicant: Professor Dr. Michael Kohler
• Subject Area: Mathematics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 449102119

We consider image classifiers based on convolutional neural networks. Our aim is to derive rate of convergence results for the difference between the misclassification risk of the classifier and the optimal misclassification risk. We introduce new assumptions on the structure and the smoothness of the aposteriori probability of class 1 and use them to study the rate of convergence of image classifiers based on suitably defined convolutional neural networks. The goal is to identify topologies of the convolutional neural networks which lead to rates of convergence independent of the dimension of the image, and to verify via simulations that these convolutional neural networks also achieve good results in applications. So the theoretical considerations in this proposal will help to identify useful topologies for convolutional neural networks in applications.

• DFG Programme: Research Grants