Jianqing Fan
Princeton University
3:45 PM
127 Hayes-Healy
A reception will precede the event at 3:15 pm in 101A Crowley Hall
FAST-NN for Big Data Modeling
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 a new 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.)
Jianqing Fan is Frederick L. Moore Professor of Finance, Professor of Operations Research and Financial Engineering, Former Chairman of Department of Operations Research and Financial Engineering and Director of Committee of Statistical Studies at Princeton University, where he directs both financial econometrics and statistics labs. After receiving his Ph.D. from the University of California at Berkeley, he has been appointed as assistant, associate, and full professor at the University of North Carolina at Chapel Hill (1989-2003), professor at the University of California at Los Angeles (1997-2000), professor and chair at Chinese University of Hong Kong, and professor at the Princeton University (2003--). He was the past president of the Institute of Mathematical Statistics (IMS) and International Chinese Statistical Association (ICSA). He is the joint editor of Journal of American Statistical Association (JASA), and was the co-editor of The Annals of Statistics, Probability Theory and Related Fields, Econometrics Journal, Journal of Econometrics, and Journal of Business and Economics Statistics.
His published work on statistics, machine learning, economics, finance, and computational biology has been recognized by The 2000 COPSS Presidents' Award, The 2007 Morningside Gold Medal of Applied Mathematics, Guggenheim Fellow in 2009, P.L. Hsu Prize in 2013, Royal Statistical Society Guy medal in silver in 2014, Noether Distinguished Scholar Award in 2018, and election to Academician of Academia Sinica and fellow of American Associations for Advancement of Science (AAAS), Institute of Mathematical Statistics (IMS), American Statistical Association (ASA), and Society of Financial Econometrics (SoFiE). His research interest includes high-dimensional statistics, machine learning, financial econometrics, and computational biology.
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