Trustworthy machine learning and uncertainty quantification

In the era of big data, massive and high-dimensional datasets have become ubiquitous. While simple statistical models often fall short in capturing the complexity of real-world problems, complex machine learning algorithms are increasingly deployed in high-stakes applications. However, the lack of interpretability of these black-box models has raised significant societal concerns regarding their trustworthiness and accountability. To develop trustworthy machine learning algorithms and conduct valid inference for the underlying association, this thesis studies the following three problems:1. In the first part of the thesis, we develop an optimal framework for binary classification under group fairness constraints. The proposed method provides finite-sample, distribution-free theoretical guarantees and applies to both group-aware and group-blind scenarios.2. In the second part, we introduce a novel framework for hallucination detection in large language models. We propose a new method with rigorous finite-sample and distribution-free guarantees for reliable detection.3. In the third part, we consider high-dimensional binary models and present a novel inference method for misspecified sparsity-constrained generalized linear models, without imposing assumptions on the underlying model-generating processes.