Learning with Confidence: Bootstrapping Error Estimates for Stochastic Iterative Algorithms

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In this age of large-scale high-dimensional data analysis, stochastic iterative optimization methods constitute a popular class of algorithms, which look at one data point at a time. These algorithms are increasingly entrusted with decision-making tasks, from discarding emails as spam to recommending routes when one drives to work, to the future decisions made by self-driving cars and medical images produced for diagnostic purposes. These applications give rise to noisy data resulting from measurement errors and variability in the experimental setup or environment. Despite this, almost all current theoretical results focus on the accurate estimation of underlying parameters. However, it is crucial to pay attention to confidence intervals that quantify the variability of the learned parameters, which allows one to make decisions with confidence. This research will develop a mathematical framework for the estimation of uncertainty of a broad class of stochastic iterative optimization methods. This project will also help train graduate students and postdoctoral scholars in uncertainty estimation for large-scale learning problems, thus making them better prepared for careers in both industry and academia. The investigators will establish central limit theorems and consistent online bootstrap procedures for fundamental stochastic iterative learning algorithms, incorporate these algorithms in software packages, and develop a framework for assessing confidence in point estimate predictions in a broad range of applications. These goals will be achieved using a variety of recently developed tools, including concentration inequalities for products of random matrices, high dimensional statistics, and theoretical advances in deep learning optimization methods.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.