Statistical guarantees for regularized neural networks

Neural networks have become standard tools in the analysis of data, but they lack comprehensive mathematical theories. For example, there are very few statistical guarantees for learning neural from especially classes estimators that used practice or at least similar to such. In this paper, we develop a general guarantee consist least-squares term and regularizer. We then exemplify with ?1-regularization, showing corresponding prediction error increases most logarithmically total number parameters can even decrease layers. Our results establish basis regularized estimation networks, deepen our understanding deep more generally.