HKU IDS Scholar Seminar Series #26:
Predictability of Complex Systems: A Statistical Physics Approach to Understanding Prediction Limits
Abstract
In this seminar, we present a statistical physics framework to establish the fundamental limits of predictability in complex systems. We map machine learning problems—specifically binary classification and link prediction—onto Spin Glass Models to analyze their theoretical boundaries.
We demonstrate that for binary classification, the upper bound of predictability is determined solely by data organization. Specifically, we prove that predictability increases as the overlap between positive and negative samples decreases, and that this limit is invariant to feature transformations. Furthermore, we extend our theory to non-Euclidean data by decomposing the predictability of complex networks into the average contribution of individual links.
Our work bridges statistical physics and machine learning to provide a unified understanding of the ultimate limits of prediction.
We demonstrate that for binary classification, the upper bound of predictability is determined solely by data organization. Specifically, we prove that predictability increases as the overlap between positive and negative samples decreases, and that this limit is invariant to feature transformations. Furthermore, we extend our theory to non-Euclidean data by decomposing the predictability of complex networks into the average contribution of individual links.
Our work bridges statistical physics and machine learning to provide a unified understanding of the ultimate limits of prediction.
Publication Note
This seminar is based on Prof Qingpeng ZHANG’s recent publication in PNAS, with Dr Fei JING—his Postdoctoral Fellow at IDS—as first author. Prof ZHANG will give a detailed account of the paper and its theoretical framework for understanding the predictability limits of complex systems.
Speaker
Prof Qingpeng ZHANG
Associate Professor @ HKU IDS & HKUMed Prof Qingpeng ZHANG is an Associate Professor at the Musketeers Foundation Institute of Data Science and the Department of Pharmacology and Pharmacy, LKS Faculty of Medicine, University of Hong Kong. His research lies at the intersection of data science and medicine, with a focus on developing interpretable machine learning and evolutionary modeling to understand complex biological systems. His work has appeared in journals such as Nature Human Behaviour, Nature Communications, and PNAS, and has been highlighted in media outlets such as The Washington Post, The New York Times, The Times, CNN, and BBC. For full biography of Prof. Zhang, please refer to: https://datascience.hku.hk/people/qingpeng-zhang/
Moderator
Prof Alec KIRKLEY
Assistant Professor @ HKU IDS & DUPAD Professor Alec Kirkley is a physicist interested in the theory of complex networks, statistical physics, as well as their applications to urban and social systems. The mathematical and computational methods he develops in his research draw on ideas from a range of disciplines including statistical physics, information theory, Bayesian inference, scientific computing, and machine learning. He received his PhD in Physics at the University of Michigan in 2021 under the supervision of Mark Newman and joined HKU as an Assistant Professor in 2022. His main research interests lie in developing principled unsupervised learning methods for noisy network data and improving the efficiency and interpretability of statistical inference methods for networks. He also adapts and applies these techniques to uncover new insights about the structure and dynamics of urban mobility as well as the underlying topology of geographical data. For full biography of Prof. Kirkley, please refer to: https://datascience.hku.hk/people/alec-kirkley/
