# Online Linearized LASSO

arXiv: https://arxiv.org/abs/2211.06039 · HTML: https://mlsanity.com/paper/2211.06039/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 11 Nov 2022.

## Builds on (most cited first, 2 of 2)

- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [Adaptive Feature Selection: Computationally Efficient Online Sparse Linear Regression under RIP](https://mlsanity.com/paper/1706.04690/) (2017)

## Built on by (most cited first, 3 of 3)

- [A Polynomial-time Algorithm for Online Sparse Linear Regression with Improved Regret Bound under Weaker Conditions](https://mlsanity.com/paper/2510.27177/) (2025)
- [OLR-WAA: Adaptive and Drift-Resilient Online Regression with Dynamic Weighted Averaging](https://mlsanity.com/paper/2512.12779/) (2025)
- [Online Generalized Sparse Regression: How Does Overparametrization Help?](https://mlsanity.com/paper/2608.17466/) (2026)

## Abstract (arXiv)

Sparse regression has been a popular approach to perform variable selection and enhance the prediction accuracy and interpretability of the resulting statistical model. Existing approaches focus on offline regularized regression, while the online scenario has rarely been studied. In this paper, we propose a novel online sparse linear regression framework for analyzing streaming data when data points arrive sequentially. Our proposed method is memory efficient and requires less stringent restricted strong convexity assumptions. Theoretically, we show that with a properly chosen regularization parameter, the ℓ2-norm statistical error of our estimator diminishes to zero in the optimal order of tildeO(√s/t), where s is the sparsity level, t is the streaming sample size, and tildeO(·) hides logarithmic terms. Numerical experiments demonstrate the practical efficiency of our algorithm.