High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether...

High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether...

Harry Markowitz introduced the Modern Portfolio Theory (MPT) for the first time in 1952 which has been applied widely for optimal portfolio selection until now. However, the theory still has some limitations that come from the instability of covariance matrix input. This leads the selected...

Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for sparse deep learning. In contrast to previous work, we...

Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for sparse deep learning. In contrast to previous work, we...