CME 510: Linear Algebra and Optimization Seminar

This seminar series highlights recent developments in numerical linear algebra and numerical optimization. The goal is to bring together scientists from different theoretical and application areas to solve complex scientific computing problems. Presenters include academic researchers and industrial R&D staff.

Wednesday March 12, 2025    4:30--5:30pm, Building 300-303  (behind the church toward the Clock Tower)   

Prof Robert Tibshirani, Department of Biomedical Data Science and Statistics, Stanford University  

Title:   Univariate guided sparse regression 

In this talk, we introduce "UniLasso''---a novel statistical method for sparse regression.  This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude.  Both of these properties are attractive for stability and interpretation of the model. Through comprehensive simulations and applications to real-world datasets, we demonstrate that UniLasso outperforms Lasso in various settings, particularly in terms of sparsity and model interpretability.  We prove asymptotic support recovery and mean-squared error consistency under a set of conditions different from the well-known irrepresentability conditions for the Lasso.  Extensions to generalized linear models (GLMs) and Cox regression are also discussed. A special case of Lasso---"uniReg"---is an interesting competitor to good old least squares regression (Legendre, 1805).

This is joint work with Sourav Chattejee and Trevor Hastie. 

Speaker Bio: Robert Tibshirani is a Professor of Biomedical Data Science, and of Statistics, at Stanford University.  He has made important contributions to the statistical analysis of complex datasets.  Some of his most well-known contributions are the Lasso, which uses L1 penalization in regression and related problems, generalized additive models and Significance Analysis of Microarrays (SAM).  He also co-authored five widely used books ‘Generalized Additive Models’, ‘An Introduction to the Bootstrap’, ‘The Elements of Statistical Learning’, ‘An Introduction to Statistical learning’, and ‘Sparsity in Statistics: the Lasso and its generalizations’.  He is an active collaborator with many scientists at Stanford Medical school.