Statistics Colloquium Series

Date: 

Monday, November 7, 2022, 12:00pm to 1:00pm

Location: 

Science Center, Room 316

Our upcoming event for the Statistics Department Colloquium Series is scheduled for this Monday, November 7th from 12:00 – 1:00pm (ET) and will be an in-person presentation Science Center Rm. 316. The speaker will be Jianqing Fan who is a Frederick L. Moore Professor of Finance, Professor of Operations Research and Financial Engineering at Princeton University.

Title: Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression

Abstract: We introduce a Factor Augmented Sparse Throughput (FAST) model that utilizes both latent factors and sparse idiosyncratic components for nonparametric regression.  The FAST model bridges factor models on one end and sparse nonparametric models on the other end.  It encompasses structured nonparametric models such as factor augmented additive model and sparse low-dimensional nonparametric interaction models and covers the cases where the covariates do not admit factor structures.  Via diversified projections as estimation of latent factor space, we employ truncated deep ReLU networks to nonparametric factor regression without regularization and to more general FAST model using nonconvex regularization, resulting in factor augmented regression using neural network (FAR-NN) and FAST-NN estimators respectively. We show that FAR-NN and FAST-NN estimators adapt to unknown low-dimensional structure using hierarchical composition models in nonasymptotic minimax rates. We also study statistical learning for the factor augmented sparse additive model using a more specific neural network architecture.  Our results are applicable to the weak dependent cases without factor structures. In proving the main technical result for FAST-NN, we establish new a deep ReLU network approximation result that contributes to the foundation of neural network theory.  Our theory and methods are further supported by simulation studies and an application to macroeconomic data.   (Joint work with Yihong Gu).