# Adaptive debiased SGD in high-dimensional GLMs with streaming data

arXiv: https://arxiv.org/abs/2405.18284 · HTML: https://mlsanity.com/paper/2405.18284/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 10 of 10)

- [Statistical Inference for Model Parameters in Stochastic Gradient Descent](https://mlsanity.com/paper/1610.08637/) (2016)
- [A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models](https://mlsanity.com/paper/1412.8765/) (2014)
- [Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods](https://mlsanity.com/paper/2102.03389/) (2021)
- [Online Debiasing for Adaptively Collected High-dimensional Data with Applications to Time Series Analysis](https://mlsanity.com/paper/1911.01040/) (2019)
- [Post-Selection Inference for Generalized Linear Models with Many Controls](https://mlsanity.com/paper/1304.3969/) (2013)
- [Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models](https://mlsanity.com/paper/1805.06970/) (2018)
- [Inference for the Case Probability in High-dimensional Logistic Regression](https://mlsanity.com/paper/2012.07133/) (2020)
- [Online Estimation for Functional Data](https://mlsanity.com/paper/2111.02750/) (2021)
- [Optimal One-pass Nonparametric Estimation Under Memory Constraint](https://mlsanity.com/paper/2208.08668/) (2022)
- [Real-Time Regression Analysis of Streaming Clustered Data With Possible Abnormal Data Batches](https://mlsanity.com/paper/2106.15794/) (2021)

## Built on by (most cited first, 1 of 1)

- [High-dimensional online learning via asynchronous decomposition: Non-divergent results, dynamic regularization, and beyond](https://mlsanity.com/paper/2603.20696/) (2026)

## Abstract (arXiv)

Online statistical inference facilitates real-time analysis of sequentially collected data, making it different from traditional methods that rely on static datasets. This paper introduces a novel approach to online inference in high-dimensional generalized linear models, where we update regression coefficient estimates and their standard errors upon each new data arrival. In contrast to existing methods that either require full dataset access or large-dimensional summary statistics storage, our method operates in a single-pass mode, significantly reducing both time and space complexity. The core of our methodological innovation lies in an adaptive stochastic gradient descent algorithm tailored for dynamic objective functions, coupled with a novel online debiasing procedure. This allows us to maintain low-dimensional summary statistics while effectively controlling the optimization error introduced by the dynamically changing loss functions. We establish the asymptotic normality of our proposed Adaptive Debiased Lasso (ADL) estimator. We conduct extensive simulation experiments to show the statistical validity and computational efficiency of our ADL estimator across various settings. Its computational efficiency is further demonstrated via a real data application to the spam email classification.