Statistics Seminar - Spring 2025
Seminars are held on Thursdays from 4:00 - 5:00pm in Room 611 and/or on Zoom unless otherwise noted. For access information, please contact the Math Department.
For questions about the seminar schedule, please contact Chong Jin and/or Chenlu Shi.
March 27
Dr. Zhaonan Qu, Columbia University
Distributionally Robust Instrumental Variables Estimation
Instrumental variables (IV) estimation is a fundamental method in econometrics and statistics for estimating causal effects in the presence of unobserved confounding. However, challenges such as untestable model assumptions and poor finite sample properties have undermined its reliability in practice. Viewing common issues in IV estimation as distributional uncertainties, we propose DRIVE, a distributionally robust IV estimation method. We show that DRIVE minimizes a square root variant of ridge regularized two stage least squares (TSLS) objective when the ambiguity set is based on a Wasserstein distance. In addition, we develop a novel asymptotic theory for this estimator, showing that it achieves consistency without requiring the regularization parameter to vanish. This novel property ensures that the estimator is robust to distributional uncertainties that persist in large samples. We further derive the asymptotic distribution of Wasserstein DRIVE and propose data-driven procedures to select the regularization parameter based on theoretical results. Simulation studies demonstrate the superior finite sample performance of Wasserstein DRIVE in terms of estimation error and out-of-sample prediction. Due to its regularization and robustness properties, Wasserstein DRIVE presents an appealing option when the practitioner is uncertain about model assumptions or distributional shifts in data.
Homepage: https://zhaonanq.github.io/
April 3
Dr. Feng Ruan, Northwestern University
Layered Models can "Automatically" Discover Low-Dimensional Feature Subspaces—No Regularization Required
Layered models, such as neural networks, appear to extract meaningful features through empirical risk minimization, yet the principles behind this process remain unclear. We analyze a two-layer nonparametric regression model akin to neural networks and prove that it naturally induces dimensionality reduction by identifying feature subspaces relevant for prediction—without conventional regularizations such as nuclear norm penalties, early stopping or other algorithmic interventions. Our results explain this implicit regularization through the lens of set identifiability from the variational analysis literature, showing how "sharpness" in the optimization landscape of population objective naturally enforces low-complexity solutions in finite samples.
Homepage: https://fengruan.github.io/
April 17
Dr. Yawen Guan, Colorado State University
Title/Abstract Forthcoming
April 24
Dr. Richard Guo, University of Michigan
Title/Abstract Forthcoming
May 1
Dr. Kan Chen, Harvard University
Title/Abstract Forthcoming
Last Updated: March 21, 2025