Online high-dimensional regression requires algorithms that can update sequentially while preserving structural sparsity. We propose \textit{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.
High-dimensional categorical data arise in genetics, biomedicine, and the social sciences, yet visualization tools for such data remain far less developed than those for continuous variables. Existing methods either scale poorly, rely heavily on low-dimensional displays detached…
In high-dimensional Ising model estimation, target sample sizes are often limited, and effectively using auxiliary binary datasets of unknown relevance remains challenging. To address this, we propose Trans-Ising, a transfer learning method that combines a loss-based source scree…
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This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, wher…
Gaussian process (GP) modeling is widely used in computational science and engineering. However, fitting a GP to high-dimensional inputs remains challenging due to the curse of dimensionality. While various methods have been proposed to reduce input dimensionality, they typically…
Gold-standard phenotype labels are often unavailable at scale in electronic health record (EHR) studies because they require manual chart review. Weakly supervised phenotyping methods instead use silver-standard labels, such as diagnosis-code counts, natural language processing (…