ABSTRACT
Deep learning has achieved remarkable success in a wide range of applications and has been applied to analyzing high-dimensional complex data in many fields of scientific research. Therefore, it would be interesting to understand why deep learning has been so successful and what its main advantages are over the traditional nonparametric methods developed over the decades, if any. In this talk, we try to explain some advantages of deep learning by considering the approximation power of deep neural networks and generalization errors of deep learning methods. Using nonparametric regression and conditional generative learning as examples, we show that deep learning can mitigate the curse of dimensionality under some realistic assumptions on data distribution.