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Convolutional neural network image classifiers are defined and the rate ofconvergence of the misclassification risk of the estimates towards the optimalmisclassification risk is analyzed. Here we consider images as random variableswith values in some functional space, where we only observe discrete samples asfunction values on some finite grid. Under suitable structural and smoothnessassumptions on the functional a posteriori probability, which includes somekind of symmetry against rotation of subparts of the input image, it is shownthat least squares plug-in classifiers based on convolutional neural networksare able to circumvent the curse of dimensionality in binary imageclassification if we neglect a resolution-dependent error term. The finitesample size behavior of the classifier is analyzed by applying it to simulatedand real data.

Analysis of convolutional neural network image classifiers in a rotationally symmetric model