B0857
Title: Learning Graphical Model with Uniform Performance via Distributional Robust Optimization
Authors: Youngseok Song - EPFL (Switzerland) [presenting]
Wen Zhou - Colorado State University (United States)
Abstract: Learning large graphical models under distributional shifts such as unknown heavy-tailed contamination or latent heterogeneous sub-populations has become a major challenge in statistics and machine learning. Utilizing the Wasserstein-$2$ ball to define the shift of unknown data generation distribution from the true graph, we formulate this problem as a high-dimensional nodewise distributionally robust regression, whose computationally tractable dual problem is established as a square-root elastic net regression. We develop an iterative algorithm that lends a substantial advantage in computational time. We study the finite sample upper bounds of the graph recovering against general distributional shifts, revealing the trade-off between the distributional robustness and the convergence rates. Extensive numerical experiments, together with real data applications, demonstrate the advantage of the proposed method compared to peer methods against a variety of distributional shifts.
