This paper presents an overview of the procedures that are involved in prediction with machine learning models with special emphasis on deep learning. We study suitable objective functions for prediction in high-dimensional settings and discuss the role of regularization methods in order to...

We propose an optimal architecture for deep neural networks of given size. The optimal architecture obtains from maximizing the minimum number of linear regions approximated by a deep neural network with a ReLu activation function. The accuracy of the approximation function relies on the neural...