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- Title
Online inference with debiased stochastic gradient descent.
- Authors
Han, Ruijian; Luo, Lan; Lin, Yuanyuan; Huang, Jian
- Abstract
We propose a debiased stochastic gradient descent algorithm for online statistical inference with high-dimensional data. Our approach combines the debiasing technique developed in high-dimensional statistics with the stochastic gradient descent algorithm. It can be used to construct confidence intervals efficiently in an online fashion. Our proposed algorithm has several appealing aspects: as a one-pass algorithm, it reduces the time complexity; in addition, each update step requires only the current data together with the previous estimate, which reduces the space complexity. We establish the asymptotic normality of the proposed estimator under mild conditions on the sparsity level of the parameter and the data distribution. Numerical experiments demonstrate that the proposed debiased stochastic gradient descent algorithm attains nominal coverage probability. Furthermore, we illustrate our method with analysis of a high-dimensional text dataset.
- Subjects
TIME complexity; ASYMPTOTIC normality; ONLINE algorithms; DATA distribution; INFERENTIAL statistics
- Publication
Biometrika, 2024, Vol 111, Issue 1, p93
- ISSN
0006-3444
- Publication type
Article
- DOI
10.1093/biomet/asad046