# Online Statistical Inference for Parameters Estimation with Linear-Equality Constraints

arXiv: https://arxiv.org/abs/2105.10315 · HTML: https://mlsanity.com/paper/2105.10315/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 26 references that are in the map.
- First posted on arXiv 21 May 2021.

## Builds on (most cited first, 4 of 4)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [SGD: General Analysis and Improved Rates](https://mlsanity.com/paper/1901.09401/) (2019)
- [Statistical Inference for Model Parameters in Stochastic Gradient Descent](https://mlsanity.com/paper/1610.08637/) (2016)
- [Statistical inference using SGD](https://mlsanity.com/paper/1705.07477/) (2017)

## Built on by (most cited first, 2 of 2)

- [Statistical Inference with Stochastic Gradient Methods under φ-mixing Data](https://mlsanity.com/paper/2302.12717/) (2023)
- [Semiparametric Regression for Spatial Data via Deep Learning](https://mlsanity.com/paper/2301.03747/) (2023)

## Abstract (arXiv)

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.