Event Date
Speaker: Jinchi Lv (Professor and Chair, Data Sciences and Operations, University of Southern California)
Title: "SOFARI-R: High-Dimensional Manifold-Based Inference for Latent Responses"
Abstract: Data reduction with uncertainty quantification plays a key role in various multi-task learning applications, where large numbers of responses and features are present. To this end, a general framework of high-dimensional manifold-based SOFAR inference (SOFARI) was introduced recently in Zheng, Zhou, Fan and Lv (2024) for interpretable multi-task learning inference focusing on the left factor vectors and singular values exploiting the latent singular value decomposition (SVD) structure. Yet, designing a valid inference procedure on the latent right factor vectors can be even more challenging compared to that on the left ones since the left factor vectors as nuisance parameters are generally not orthogonal to each other due to the correlated predictors. To tackle these issues, in this paper we suggest a new method of high-dimensional manifold-based SOFAR inference for latent responses (SOFARI-R). By appropriately rescaling the latent factor vectors in the SVD decomposition and utilizing the underlying Stiefel manifold structure, coupled with an additional hard-thresholding step on the initial SOFARI estimates, the SOFARI-R produces bias-corrected estimators on the latent right factor vectors that enjoy asymptotically normal distributions with justified asymptotic variance estimates. Two variants of SOFARI-R are introduced to deal with the cases of strongly and weakly orthogonal latent factors, respectively. We demonstrate the effectiveness of the newly suggested method using extensive simulation studies and an economic application. This is a joint work with Zemin Zheng and Xin Zhou.
Bio: 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, data science, artificial intelligence, machine learning, and business applications as well as blockchain and large language models.
Faculty website (links to USC): http://faculty.marshall.usc.edu/jinchi-lv/