Adaptive Iterative Hard Thresholding for Online High-dimensional Quantile Regression
Zitian Zhou, Nan Lin
stat.ML, cs.LG, stat.ME
Submitted: 2026-06-26
License: http://creativecommons.org/licenses/by/4.0/
The gist: Online high-dimensional regression requires algorithms that can update sequentially while preserving structural sparsity.
Terminology
Abstract
Online high-dimensional regression requires algorithms that can update sequentially while preserving structural sparsity. We propose Adaptive Iterative Hard Thresholding (AIHT), an online sparse-regression framework that alternates stochastic subgradient updates with adaptively scheduled hard-thresholding steps. The key idea is to separate support discovery from local refinement: early in the learning process, AIHT delays thresholding so that weak but informative coordinates have time to accumulate signal, while later it increases the projection frequency to stabilize the sparse estimator and exploit local curvature. We develop the theory for high-dimensional online quantile regression, a challenging setting in which the loss is nonsmooth and the data may exhibit heterogeneity or heavy-tailed noise. Under restricted curvature and gradient-leakage conditions, AIHT remains in an inflated sparse cone, exhibits a two-phase convergence behavior, and attains logarithmic regret for the sliding-window objective. Simulations for online quantile regression, together with threshold-scheduling ablations, support the proposed mechanism and illustrate its advantage over standard online sparse-learning baselines.
Related papers
- Behavior of prediction performance metrics with rare events
- Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
- A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
- Scalable Posterior Uncertainty for Flexible Density-Based Clustering
- A Transport Geometry of Benign Overfitting
- Efficient quadratic entropy with distance sketches