Understanding generalization and consistency of DCNN from weak dependence perspective

In this article we establish an unified framework on the generalization ability of deep convolutional neural networks (DCNN) such that it contains both the setting of independent and identically distributed (i.i.d.) sample and the cases of non-independent sample such as strongly mixing, Markov chain and Gaussian process. The established generalization bound of DCNN is obvious dependent on the data dependence of the given training data and a novel necessary condition on the consistency of DCNN is presented. To improve the performance of DCNN, a new DCNN based on a modified loss function is proposed. The established results are extended to the cases of non-stationary data. The performance of the proposed DCNN is verified by some numerical experiments.