{"id":862,"date":"2024-12-11T11:08:14","date_gmt":"2024-12-11T11:08:14","guid":{"rendered":"https:\/\/sites.rutgers.edu\/nawaf-bou-rabee\/?p=862"},"modified":"2024-12-11T11:17:33","modified_gmt":"2024-12-11T11:17:33","slug":"why-go-coordinate-free-in-monte-carlo-and-optimization","status":"publish","type":"post","link":"https:\/\/sites.rutgers.edu\/nawaf-bou-rabee\/why-go-coordinate-free-in-monte-carlo-and-optimization\/","title":{"rendered":"Why Go Coordinate-Free in Monte Carlo and Optimization?"},"content":{"rendered":"

Traditional methods like Gibbs sampling or randomized Kaczmarz rely heavily on specific coordinate systems, which can limit their efficiency\u2014especially in ill-conditioned settings. But what happens when we step away from these constraints and adopt a coordinate-free approach?<\/p>\n

Our latest research examines this question, rigorously exploring the advantages and limitations of coordinate-free methods for both sampling and optimization. While Hit-and-Run has long been recognized as a coordinate-free Gibbs sampler, its quantitative benefits over coordinate-bound methods have remained largely unexplored\u2014until now.<\/p>\n

In collaboration with Andreas Eberle and Stefan Oberd\u00f6rster (both from the University of Bonn), we rigorously analyze and quantify the performance of coordinate-free methods like Hit-and-Run and a coordinate-free randomized Kaczmarz algorithm, identifying the settings where these methods excel.<\/p>\n

\u2728 Mathematical Insights<\/p>\n