Information Theory for Trustworthy Machine Learning

Abstract

In this thesis, we provide an information-theoretic foundation for trustworthy machine learning (ML). ML algorithms are increasingly used in applications of significant social consequences. It is crucial to ensure that these algorithms are not just accurate but also generalizable, fair, and privacy-preserving. We develop new information-theoretic tools for proving rigorous performance guarantees for practical ML models and establishing protocols to ensure the responsible use of data. Towards rigorous performance guarantees, we derive generalization bounds for understanding the behaviors of complex ML models (e.g., neural networks). In particular, we study how the interaction between data distributions and optimization methods influences generalization. We consider a family of optimization methods---noisy iterative algorithms---and investigate their generalization capability. We derive distribution-dependent generalization bounds by connecting noisy iterative algorithms with additive noise channels found in information theory. Numerical experiments demonstrate that our results can help understand many empirical observations of neural networks. Towards responsible use, we characterize a fundamental limit of algorithmic fairness and privacy. Specifically, we provide conditions that ensure fair use of group attributes and analyze the "best" privacy-utility trade-offs among all privacy-preserving mechanisms. These theoretical results, in turn, inspire new algorithms that can repair unfair models or preserve privacy in data sharing. Finally, we evaluate the robustness of information-theoretic privacy measures and establish statistical consistency of "optimal" privacy mechanisms.