Abstract: In this talk, we consider multivariate regression with hidden variables, $Y = \Theta^TX + B^TZ  + E$, where $Y$ is a $m$-dimensional response vector, $X$ is a $p$-dimensional vector of observable features, $Z$ represents a $K$-dimensional vector of unobserved hidden variables, possibly correlated with $X$, and $E$ is an independent error. The number of hidden variables $K$ is unknown and both $m$ and $p$ are allowed (but not required) to grow with the sample size $n$. We address several fundamental challenges of this problem, (1) parameter identification, (2) estimation methods/non-asymptotic analysis, (3) asymptotic inference, and (4) generalizations to heteroscedastic errors and GLM. This talk is based on a sequence of works primarily with my students. Related papers include  https://arxiv.org/abs/2003.13844,  https://arxiv.org/pdf/2201.08003, https://arxiv.org/abs/2509.00196.

Bio: Dr. Ning is an associate professor in the Department of Statistics and Data Science at Cornell University. He received his Ph.D in Biostatistics from the Johns Hopkins University and was a post-doc at Princeton University and University of Waterloo. His research interests focus on high-dimensional statistics, and statistical inference in machine learning problems.