Trustworthy AI Through Principled Advances in Machine Unlearning, Algorithmic Bias Mitigation, and Explainability

In an era of unprecedented advances in Machine Learning and Artificial Intelligence, concerns are rising about the trustworthiness of these systems. Trustworthy AI is a multidimensional concept, which the EU High-Level Expert Group on Artificial Intelligence characterizes through three key pillars: Lawfulness, referring to the legal compliance and regulatory alignment of AI models; Ethics, concerning their adherence to ethical principles such as fairness and accountability; and Robustness, denoting their reliability, resilience, and safety under real-world conditions, including distributional shifts and evolving deployment environments. In this thesis, we introduce principled advances across all three dimensions of Trustworthy AI. For Lawfulness, we rationalize and extend the growing literature on Machine Unlearning, proposing a unified and easily extensible framework, called ERASURE, from which we derive a more coherent theoretical and empirical framing, alongside a state of the art advancement through the study of an orthogonal problem called Forget Set Identification. For Ethics, we conduct an empirical investigation into data fairness in Software engineering, identifying structural sources of bias, and we introduce a state of the art debiasing method that substantially mitigates bias at the data level. Finally, for Robustness, we examine dense information retrieval systems powered by large language models, proposing a technique, called DbU-Cloud, that enhances their explainability while preserving or improving retrieval performance. Collectively, these contributions represent a significant advancement toward building legally compliant, privacy-preserving, and trustworthy AI systems.