2023/02/24 by Ruiqi Liu, Xi Chen, Liu, Ruiqi +3 · 1 citation
Computer Science · Mathematics · #62F12 #62F40 #62M10 #FOS: Computer and information sciences #Machine Learning (stat.ML) #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2302.12717
openalex publication_date 2023/02/24 · openalex created_date 2023/03/01 · openalex updated_date 2026/07/29
Stochastic gradient descent (SGD) is a scalable and memory-efficient optimization algorithm for large datasets and stream data, which has drawn a great deal of attention and popularity. The applications of SGD-based estimators to statistical inference such as interval estimation have also achieved great success. However, most of the related works are based on i.i.d. observations or Markov chains. When the observations come from a mixing time series, how to conduct valid statistical inference remains unexplored. As a matter of fact, the general correlation among observations imposes a challenge on interval estimation. Most existing methods may ignore this correlation and lead to invalid confidence intervals. In this paper, we propose a mini-batch SGD estimator for statistical inference when the data is ϕ-mixing. The confidence intervals are constructed using an associated mini-batch bootstrap SGD procedure. Using ``independent block'' trick from \citeyu1994rates, we show that the proposed estimator is asymptotically normal, and its limiting distribution can be effectively approximated by the bootstrap procedure. The proposed method is memory-efficient and easy to implement in practice. Simulation studies on synthetic data and an application to a real-world dataset confirm our theory.