BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Bridging Machine Learning\, Dynamical Systems\, and Algorithmic In formation Theory: Insights from Sparse Kernel Flows\, PoincarĂ© Normal For ms and PDE Simplification - Boumediene Hamzi (CALTECH (California Institut e of Technology)) DTSTART:20250527T093000Z DTEND:20250527T103000Z UID:TALK232516@talks.cam.ac.uk DESCRIPTION:In this talk\, we explore how Machine Learning (ML) and Algori thmic Information Theory (AIT)\, though emerging from different traditions \, can mutually inform one another in the following directions:\n\nAIT for Kernel Methods: We investigate how AIT concepts inspire the design of ker nels that integrate principles such as Kolmogorov complexity and Normalize d Compression Distance (NCD). We propose a novel clustering method based o n the Minimum Description Length (MDL) principle\, implemented via K-means and Kernel Mean Embedding (KME). Additionally\, we employ the Loss Rank P rinciple (LoRP) to learn optimal kernel parameters for Kernel Density Esti mation (KDE)\, extending AIT-inspired techniques to flexible\, nonparametr ic models.\nKernel Methods for AIT: We also demonstrate how kernel methods can approximate AIT measures such as NCD and Algorithmic Mutual Informati on (AMI)\, offering new tools for compression-based analysis. In particula r\, we show that the Hilbert-Schmidt Independence Criterion (HSIC) can be interpreted as an approximation to AMI\, providing a robust theoretical ba sis for clustering and dependence measurement.\n\nFinally\, we illustrate how techniques from ML and Dynamical Systems (DS)&mdash\;including Sparse Kernel Flows\, Poincaré\; Normal Forms\, and PDE Simplification&mdas h\; can be reformulated through the lens of AIT.Our results suggest that k ernel methods are not just flexible tools in ML&mdash\; they can serve as conceptual bridges across AIT\, ML\, and DS\, leading to more unified and interpretable approaches to unsupervised learning\, the analysis of dynami cal systems\, and model discovery.This work is based on the following pape rs\n\nBoumediene Hamzi\, Marcus Hutter\, Houman Owhadi\, Bridging Algorith mic Information Theory and Machine Learning: Clustering\, Density Estimati on\, Kolmogorov Complexity-Based Kernels\, and Kernel Learning in Unsuperv ised Learning.\nBoumediene Hamzi\, Marcus Hutter\, Houman Owhadi\, Bridgin g Algorithmic Information Theory and Machine Learning: A New Approach to K ernel Learning.\nJonghyeon Lee\, Boumediene Hamzi\, Yannis Kevrekidis\, Ho uman Owhadi\, Gaussian Processes Simplify Differential Equations.\nLu Yang \, Xiuwen Sun\, Boumediene Hamzi\, Houman Owhadi\, Naiming Xie\, Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective\, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systems.\n LOCATION:Seminar Room 2\, Newton Institute END:VEVENT END:VCALENDAR