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Statistical Physics For Optimization and Learning

A Set of Lectures given at Duke in 2018 by Lenka Zdeborova and Florent Krzakala

Main topics

Interest in the methods and concepts of statistical physics is rapidly growing in fields as diverse as theoretical computer science, probability, machine learning, discrete mathematics, optimization and compressed sensing. This course will cover this rich and active interdisciplinary research landscape.

More specifically, we will review the statistical physics approach to problems ranging from graph theory (percolation, community detection) to discrete optimization and constraint satisfaction (satisfiability, coloring, bisection) and to inference and learning problems (learning in neural networks, clustering of data and of networks, compressed sensing or sparse linear regression, low-rank matrix and tensor factorization, etc.).

We will expose theoretical methods of analysis (replica, cavity, …) algorithms (message passing, spectral methods, …), discuss concrete applications, highlight rigorous justifications as well as present the connection to the physics of glassy and disordered systems.

The course is designed to be accessible to graduate students and researchers of all natural science and engineering disciplines with a basic knowledge of probability and analysis. Advanced training in any of the above fields is not requisite.

References: Information, Physics and Computation (Oxford Graduate Texts), 2009, M. Mézard, A. Montanari

Statistical Physics of inference: Thresholds and algorithms, Advances in Physics 65, 5 2016, L. Zdeborová & F. Krzakala

Many thanks to Mengke Lian who has been an amazing TA for this lecture.

Overleaf lecture notes: the lectures notes of the course has freely avaliable on overleaf

Exercices: all the assigments and corrections are avaliable on github

Jupyter notebook tutorials: all the tutorial are avaliable on github

Download the poster annoucement