Boumediene Hamzi

Early career

Temporary Assistant Professor at the University of Paris-Sud/Orsay, an INRIA Research Fellow, and a Research Assistant Professor at UCDavis (CA), and subsequent positions at the Mathematical Sciences Research Institute in Berkeley, Duke University, and the Fields Institute in Toronto. Most recently, I served as a visiting professor at Johns Hopkins University.

Research

Throughout my research career, I have sought to answer the pivotal question: How can complex systems be effectively analyzed? My investigations have branched into three key approaches:

1. Dynamical Systems Theory (DST): This approach allows for the analysis of complex systems when the model is known. It offers nontrivial ways to analyze dynamical systems. It has the status of Theory, but it is currently limited to low-dimensional and some classes of infinite-dimensional dynamical systems. 

2. Machine Learning (ML): ML is concerned with designing algorithms that accomplish tasks, improving as they process more data. It's particularly useful for analyzing high-dimensional complex systems where the model is unknown. However, its theoretical framework is still missing, and it lacks clear methodologies, making it unclear why certain algorithms work and their domain of applicability. 

3. Algorithmic Information Theory (AIT): AIT provides a framework for understanding concepts such as complexity, induction, simplicity, randomness, and information content. It's a robust theoretical approach but faces practical challenges in computing the involved quantities.

My previous research interests focused on "Dynamical Theory of Control'' that is Control Theory from the point of view of the theory of dynamical systems where the goal is the integration of concepts and ideas from dynamical systems theory and control theory into a framework that allows to develop both theories, emphasizing the analysis and control of systems with bifurcations.

My current research interests are at the intersection(s) of Machine Learning, Dynamical Systems, and Algorithmic Information Theory in view of developing a theoretical framework for Machine Learning in the following directions.

• Machine Learning for Dynamical Systems: This involves analyzing dynamical systems based on observed data rather than analytical study, aiming to extend classical theory and develop a qualitative theory in reproducing kernel Hilbert spaces.

• Dynamical Systems for Machine Learning: Here, I look at analyzing ML algorithms using dynamical systems theory tools by considering ML algorithms as dynamical systems, aiming to understand these algorithms' potential and limitations and establish a solid theoretical foundation.

• Machine Learning for Algorithmic Information Theory: This direction explores using ML to approach problems in AIT, including applications of Solomonoff induction and algorithmic probability, and developing ML algorithms for better compression and prediction to approximate Kolmogorov Complexity.

• Algorithmic Information Theory for Machine Learning: This involves reformulating and analyzing ML algorithms using AIT tools to understand their potential, limits, and applicability domain. This helps in understanding why certain ML methods  will a priori work or not work well for specific problems.

Publications

Most of my papers are on Research Gate, ORCID, and Google Scholar.

I led different talks and symposia. I am the Organizer of the "Machine Learning and Dynamical Systems" seminar series. I am also a Co-Organizer of the One World Seminar Series on the Mathematics of Machine Learning. I was the lead organizer of the following events.

A full list of recordings is available here.