Dissertation Defense Talks
PhD students in the Department of Statistics and Data Science give a talk that is open to Northwestern faculty and graduate students as part of their dissertation defense.
Fall 2023 dissertation defense talks
Optimization, Sampling and Their Interplay: Theory and Applications to Statistics and Machine Learning
Date: Friday, November 10, 2023
Location: University Hall 102
Speaker: Tim Tsz-Kit Lau, PhD candidate
Abstract: Optimization and sampling are two main pillars of modern high-dimensional statistics and machine learning, and more broadly, data science. Optimization theory and algorithms have been heavily involved in the development of numerical solvers for high-dimensional statistical estimation problems under the frequentist paradigm as well as the success of deep learning, whereas efficient sampling procedures have been the major workhorse of Bayesian inference and uncertainty quantification. Leveraging the recently revived and intriguing connection between optimization and sampling, I study the theoretical underpinning in their interplay, and develop novel algorithms for applications to statistics and machine learning. In particular, I address two intrinsic issues arising in both high-dimensional statistical estimation and sampling problems—"nonsmoothness'' and "nonconvexity'', which are exacerbated by the notoriously inevitable "curse of dimensionality'' brought by massive datasets and gigantic models, employing tools from convex optimization and diffusion processes. Finally, I also explore the use of deep learning to develop novel estimation procedures for various high-dimensional regularized M-estimation problems.