Online Covariance Matrix Estimation in Stochastic Gradient Descent

The stochastic gradient descent (SGD) algorithm is widely used for parameter estimation, especially huge datasets and online learning. While this recursive popular computation memory efficiency, quantifying variability randomness of the solutions has been rarely studied. This article aims at conducting statistical inference SGD-based estimates in an setting. In particular, we propose a fully estimator covariance matrix averaged SGD (ASGD) iterates only using from SGD. We formally establish our estimator’s consistency show that convergence rate comparable to offline counterparts. Based on classic asymptotic normality results ASGD, construct asymptotically valid confidence intervals model parameters. Upon receiving new observations, can quickly update estimate intervals. approach fits setting takes full advantage SGD: efficiency memory.