Online Linearized LASSO
Shuoguang Yang, Yuhao Yan, Xiuneng Zhu, Qiang Sun
Abstract
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 $\ell_2$-error of our estimator decays to zero at the optimal order of $\tilde \mathcal{O}(\frac{s}{\sqrt{t}})$, where $s$ is the sparsity level, $t$ is the streaming sample size, and $\tilde \mathcal{O}(\cdot)$ hides logarithmic terms. Numerical experiments demonstrate the practical efficiency of our algorithm.
BibTeX
@InProceedings{pmlr-v206-yang23g,
title = {Online Linearized LASSO},
author = {Yang, Shuoguang and Yan, Yuhao and Zhu, Xiuneng and Sun, Qiang},
booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {7594--7610},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/yang23g/yang23g.pdf},
url = {https://proceedings.mlr.press/v206/yang23g.html},
abstract = {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 $\ell_2$-error of our estimator decays to zero at the optimal order of $\tilde \mathcal{O}(\frac{s}{\sqrt{t}})$, where $s$ is the sparsity level, $t$ is the streaming sample size, and $\tilde \mathcal{O}(\cdot)$ hides logarithmic terms. Numerical experiments demonstrate the practical efficiency of our algorithm.}
}