Online inference with debiased stochastic gradient descent

• 成果类型: Article
• 署名作者: Han, Ruijian; Luo, Lan; Lin, Yuanyuan; Huang, Jian
• 署名单位: Hong Kong Polytechnic University; Rutgers University System; Chinese University of Hong Kong
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad046
• 发表日期: 2024
• 页码: 93108
• 关键词: confidence-intervals; approximation; parameters

摘要

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.