报告题目：Learning by Compression: From Data to Simpler Models

报告所属学科：管理科学与工程

报告人：Boumediene Hamzi（the Department of Computing and Mathematical Sciences at Caltech）

报告时间：2026年10月14日 10:00-12:00

报告地点：经管学院715室

报告摘要：

Engineers often face three related challenges: learning from limited data, selecting predictive models, and simplifying complex dynamical systems. This talk connects these challenges through a unifying idea: a good model captures essential patterns in a compact description.

Drawing on algorithmic information theory, we explore how compression relates to machine learning and model complexity. We introduce kernels designed to capture shared, compressible structures and connect their spectra to the number of bits required for function approximation, providing an information-theoretic interpretation of classical learning theory.

We then discuss model selection through the minimum description length principle, highlighting Sparse Kernel Flows and their applications to forecasting chaotic systems. We also introduce Solomonoff Gaussian processes, which favor simpler explanations for prediction and uncertainty quantification.

Finally, we examine how mathematical transformations simplify nonlinear dynamical systems, including the Cole–Hopf transformation for the Burgers equation and normal-form reductions for the Brusselator and Moore–Greitzer models. These examples illustrate how description length provides a unified perspective on learning, prediction, and model simplification.

报告人简介：

Professor Boumediene Hamzi is currently a Senior Scientist in the Department of Computing and Mathematical Sciences at Caltech, an Affiliate Fellow of the Data Science Institute at Imperial College London, and a co-leader of the Research Interest Group on Machine Learning and Dynamical Systems at the Alan Turing Institute. His research lies at the intersection of machine learning, dynamical systems, control theory, and data analysis, with a particular focus on data-driven modeling and prediction of complex nonlinear systems. More broadly, he is interested in the interplay between artificial intelligence and dynamical systems, including the use of machine learning to uncover structure from data and the application of dynamical systems theory to better understand learning algorithms. His work contributes to AI for science and to the study of complex systems in economics and finance, mathematics, and statistics.