On Constructing Confidence Region for Model Parameters in Stochastic Gradient Descent via Batch Means
This provides a computationally efficient method for uncertainty quantification in SGD, which is incremental but addresses a known bottleneck in parameter estimation for machine learning practitioners.
The paper tackles the problem of constructing confidence regions for model parameters in stochastic gradient descent by proposing a batch means method that avoids estimating the covariance matrix, establishing a functional central limit theorem for Polyak-Ruppert averaging estimators and extending batch size specifications.
In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method. The main idea is to cancel out the covariance matrix which is hard/costly to estimate. In the process of developing the algorithm, we establish process-level functional central limit theorem for Polyak-Ruppert averaging based stochastic gradient descent estimators. We also extend the batch means method to accommodate more general batch size specifications.