Image classification from independent and identically distributed random variables is considered. Image classifiers are defined which are based on a linear combination of deep convolutional networks with max-pooling layer. Here all the weights are learned by stochastic gradient descent. A general result is presented which shows that the image classifiers are able to approximate the best possible deep convolutional network. In case that the a posteriori probability satisfies a suitable hierarchical composition model it is shown that the corresponding deep convolutional neural network image classifier achieves a rate of convergence which is independent of the dimension of the images.

翻译：本文研究了从独立同分布随机变量中进行图像分类的问题。我们定义了一类基于带最大池化层的深度卷积网络线性组合的图像分类器，其中所有权重均通过随机梯度下降算法学习。我们提出了一个通用结果，表明该图像分类器能够逼近最优的深度卷积网络。当后验概率满足适当的分层组合模型时，研究证明相应的深度卷积神经网络图像分类器可获得收敛速率，且该速率与图像维度无关。