Date: 2025-10-24

Time: 15:30-16:30 (Montreal time)

Location: In person, Burnside 1104

https://mcgill.zoom.us/j/81872329544

Meeting ID: 818 7232 9544

Passcode: None

Abstract:

We study multi-task linear regression for a collection of tasks that share a latent, low-dimensional structure. Each task’s regression vector belongs to a subspace whose dimension, denoted intrinsic dimension, is much smaller than the ambient dimension. Unlike classical analyses that assume an identical subspace for every task, we allow each task’s subspace to drift from a single reference subspace by a controllable similarity radius, and we permit an unknown fraction of tasks to be outliers that violate the shared-structure assumption altogether. Our contributions are threefold. First, adaptivity: we design a penalized empirical-risk algorithm and a spectral method.  Both algorithms automatically adjust to the unknown similarity radius and to the proportion of outliers. Second, minimaxity: we prove information-theoretic lower bounds on the best achievable prediction risk over this problem class and show that both algorithms attain these bounds up to constant factors; when no outliers are present, the spectral method is exactly minimax-optimal. Third, robustness: for every choice of similarity radius and outlier proportion, the proposed estimators never incur larger expected prediction error than independent single-task regression, while delivering strict improvements whenever tasks are even moderately similar and outliers are sparse. Additionally, we introduce a thresholding algorithm to adapt to an unknown intrinsic dimension. We conduct extensive numerical experiments to validate our theoretical findings.

Speaker

Yang Feng is a Professor of Biostatistics in the School of Global Public Health at New York University, where he is also affiliated with the Center for Data Science. He earned his Ph.D. in Operations Research from Princeton University in 2010. His research centers on the theoretical and methodological foundations of machine learning, high-dimensional statistics, network models, and nonparametric statistics, with applications in Alzheimer’s disease prognosis, cancer subtype classification, genomics, electronic health records, and biomedical imaging, enabling more accurate models for risk assessment and clinical decision-making. His work has been supported by grants from the National Institutes of Health and the National Science Foundation (NSF), including the NSF CAREER Award. He currently serves as Associate Editor for several leading journals, including the Journal of the American Statistical Association (JASA), the Journal of Business & Economic Statistics, the Journal of Computational & Graphical Statistics, and the Annals of Applied Statistics. In addition, he will serve as Review Editor for JASA and The American Statistician from 2026 to 2028. His professional recognitions include being named a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, as well as an elected member of the International Statistical Institute.