Nonparametric Perspective on Deep Learning

Models built with deep neural network (DNN) can handle complicated real-world data extremely well, without suffering from the curse of dimensionality or the non-convex optimization. To contribute to the theoretical understanding of deep learning, we will investigate the nonparametric aspects of DNNs by addressing the following questions: (i) what kind of data can be best learned by deep neural networks？ (ii) can deep neural networks achieve the statistical optimality? (iii) is there any algorithmic guarantee for obtaining such optimal neural networks? Our theoretical analysis applies to two most fundamental setup in practice: regression and classification.