A1130
Title: Adaptive debiased SGD in high-dimensional GLMs with streaming data
Authors: Yuanhang Luo - Hong Kong Polytechnic University (Hong Kong) [presenting]
Ruijian Han - The Hong Kong Polytechnic University (China)
Lan Luo - Rutgers University (United States)
Yuanyuan Lin - The Chinese University of Hong Kong (Hong Kong)
Jian Huang - The Hong Kong Polytechnic University (China)
Abstract: Online statistical inference facilitates real-time analysis of sequentially collected data, making it different from traditional methods that rely on static datasets. A novel approach is introduced to online inference in high-dimensional generalized linear models, where regression coefficient estimates and their standard errors are updated upon each new data arrival. In contrast to existing methods that either require full dataset access or large-dimensional summary statistics storage, the method operates in a single-pass mode, significantly reducing both time and space complexity. The core of the methodological innovation lies in an adaptive stochastic gradient descent algorithm tailored for dynamic objective functions coupled with a novel online debiasing procedure. This allows the maintenance of low-dimensional summary statistics while effectively controlling the optimization error introduced by the dynamically changing loss functions. The asymptotic normality of the proposed adaptive debiased lasso (ADL) estimator is established. Extensive simulation experiments are conducted to show the statistical validity and computational efficiency of the ADL estimator across various settings. Its computational efficiency is further demonstrated via a real data application for spam email classification.
