Online statistical inference for parameters estimation with linear-equality constraints
Document Type
Article
Publication Date
9-1-2022
Abstract
Stochastic gradient descent (SGD) and projected stochastic gradient descent (PSGD) are scalable algorithms to compute model parameters in unconstrained and constrained optimization problems. In comparison with SGD, PSGD forces its iterative values into the constrained parameter space via projection. From a statistical point of view, this paper studies the limiting distribution of PSGD-based estimate when the true parameters satisfy some linear-equality constraints. Our theoretical findings reveal the role of projection played in the uncertainty of the PSGD-based estimate. As a byproduct, we propose an online hypothesis testing procedure to test the linear-equality constraints. Simulation studies on synthetic data and an application to a real-world dataset confirm our theory.
Identifier
85131124157 (Scopus)
Publication Title
Journal of Multivariate Analysis
External Full Text Location
https://doi.org/10.1016/j.jmva.2022.105017
e-ISSN
10957243
ISSN
0047259X
Volume
191
Grant
DMS-1821157
Recommended Citation
Liu, Ruiqi; Yuan, Mingao; and Shang, Zuofeng, "Online statistical inference for parameters estimation with linear-equality constraints" (2022). Faculty Publications. 2683.
https://digitalcommons.njit.edu/fac_pubs/2683
