SOFARI: High-Dimensional Manifold-Based Inference



Multi-task learning is a widely used technique for harnessing information from various tasks. Recently, the sparse orthogonal factor regression (SOFAR) framework, based on the sparse singular value decomposition (SVD) within the coefficient matrix, was introduced for interpretable multi-task learning, enabling the discovery of meaningful latent feature-response association networks across different layers. However, conducting precise inference on the latent factor matrices has remained challenging due to orthogonality constraints inherited from the sparse SVD constraint. In this paper, we suggest a novel approach called high-dimensional manifold-based SOFAR inference (SOFARI), drawing on the Neyman near-orthogonality inference while incorporating the Stiefel manifold structure imposed by the SVD constraints. By leveraging the underlying Stiefel manifold structure, SOFARI provides bias-corrected estimators for both latent left factor vectors and singular values, for which we show to enjoy the asymptotic mean-zero normal distributions with estimable variances. We introduce two SOFARI variants to handle strongly and weakly orthogonal latent factors, where the latter covers a broader range of applications. We illustrate the effectiveness of SOFARI and justify our theoretical results through simulation examples and a real data application in economic forecasting. This is a joint work with Yingying Fan, Zemin Zheng and Xin Zhou.


Jinchi Lv is Kenneth King Stonier Chair in Business Administration, Department Chair, Professor in Data Sciences and Operations Department of the Marshall School of Business at the University of Southern California, and Professor in Department of Mathematics at USC. He received his Ph.D. in Mathematics from Princeton University in 2007. He was McAlister Associate Professor in Business Administration at USC from 2016-2019. His research interests include statistics, machine learning, data science, business applications, and artificial intelligence and blockchain.

His papers have been published in journals in statistics, economics, business, computer science, information theory, neuroscience, and biology. He is the recipient of Distinguished Scholar (2024, Lingnan University), NSF Grant (2023), NSF Emerging Frontiers (EF) Grant (2022), Fellow of American Statistical Association (2020), NSF Grant (2020), Kenneth King Stonier Chair in Business Administration (2019), Fellow of Institute of Mathematical Statistics (2019), Member of USC University Committee on Appointments, Promotions, and Tenure (UCAPT, 2019-present), USC Marshall Dean’s Award for Research Impact (2017), Adobe Data Science Research Award (2017), McAlister Associate Professor in Business Administration (2016), Simons Foundation Grant (2016), the Royal Statistical Society Guy Medal in Bronze (2015), NSF Faculty Early Career Development (CAREER) Award (2010), USC Marshall Dean’s Award for Research Excellence (2009), Journal of the Royal Statistical Society Series B Discussion Paper (2008), NSF Grant (2008), and Zumberge Individual Award from USC’s James H. Zumberge Faculty Research and Innovation Fund (2008). He has served as an associate editor of Operations Research (2024-present), Journal of the American Statistical Association (2023-present), Journal of Business & Economic Statistics (2018-present), The Annals of Statistics (2013-2018), and Statistica Sinica (2008-2016).