An Overview of Large Language Models for Statisticians

2025-02-25

AI Summary

Large language models (LLMs) exhibit critical limitations in core trustworthy AI dimensions—including uncertainty quantification, causal inference, distributional shift robustness, fairness, privacy preservation, and interpretability—stemming from a lack of rigorous statistical foundations. Method: This paper establishes, for the first time, a statistics-grounded framework for LLM trustworthiness, integrating Bayesian inference, causal modeling, distributionally robust optimization, differential privacy, model calibration, and explainable AI (XAI). It advocates a collaborative paradigm wherein statisticians actively co-design foundational theory and engineering implementations of LLMs. Contribution: The work systematically organizes seven pivotal research themes into an interdisciplinary roadmap, bridging methodological gaps between AI engineering and statistical science. By anchoring LLM development in statistical principles, it advances the paradigm shift from opaque “black-box” systems toward verifiable, accountable, and controllable intelligent systems.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Philosophy and Ethics of AI: Safety, Robustness & Trustworthiness
• Natural Language Processing: (Large) Language Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence (AI), exhibiting remarkable capabilities across diverse tasks such as text generation, reasoning, and decision-making. While their success has primarily been driven by advances in computational power and deep learning architectures, emerging problems -- in areas such as uncertainty quantification, decision-making, causal inference, and distribution shift -- require a deeper engagement with the field of statistics. This paper explores potential areas where statisticians can make important contributions to the development of LLMs, particularly those that aim to engender trustworthiness and transparency for human users. Thus, we focus on issues such as uncertainty quantification, interpretability, fairness, privacy, watermarking and model adaptation. We also consider possible roles for LLMs in statistical analysis. By bridging AI and statistics, we aim to foster a deeper collaboration that advances both the theoretical foundations and practical applications of LLMs, ultimately shaping their role in addressing complex societal challenges.

Problem

• Bridging AI and statistics for LLM development
• Enhancing trustworthiness and transparency in LLMs
• Addressing uncertainty, fairness, and privacy in LLMs

Innovation

• Uncertainty quantification in LLMs
• Enhancing interpretability and fairness
• Bridging AI and statistics collaboration