E2 338, Spring 2024
Mean-Field Asymptotics and Applications
Lectures
- 09 Jan 2024: Lecture-01 Continuous time Markov chains
- 11 Jan 2024: Lecture-02 Embedded Markov chain and sojourn times
- 16 Jan 2024: Lecture-03 Uniformization of Markov processes
- 18 Jan 2024: Lecture-04 Invariant distribution
- 23 Jan 2024: Lecture-05 Reversibility
- 25 Jan 2024: Lecture-06 Interacting particle dynamics
- 30 Jan 2024: Lecture-07 Mean-field models
- 01 Feb 2024: Lecture-08 Convergence to mean-field
- 06 Feb 2024: Lecture-09 Kurtz’s theorem: preliminaries
- 08 Feb 2024: Lecture-10 Kurtz’s theorem: proof
- 15 Feb 2024: Lecture-11 Behavior at stationarity
- 20 Feb 2024: Lecture-12 Stein’s method
- 22 Feb 2024: Lecture-13 Proof of convergence
- 29 Feb 2024: Lecture-14 Perturbation theory
- 05 Mar 2024: Lecture-15 The Boltzmann distribution
- 07 Mar 2024: Lecture-16 The thermodynamic limit
- 12 Mar 2024: Lecture-17 Interacting particle systems
- 14 Mar 2024: Lecture-18 Statistical decision theory
- 19 Mar 2024: Lecture-19 Free energy approach
Homework
Course Syllabus
- Replica methods in statistics physics: Basic concepts in statistical physics, Ising models, statistical decision theory, free energy approach, concentration inequalities in mean field asymptotics, field theory calculations, replica methods, LASSO risk
- Convergence of mean field limits: Conditions for mean-field convergence, proof using Stein’s method, proof using perturbation theory
- Approximate message passing (AMP) algorithms: Overview of algorithms for Gibbs mean estimators and LASSO, theoretical analysis of AMP, Markov random fields, Belief Propagation (BP) on trees, BP to message passing, MP to LASSO, Derivation of AMP from MP
- Applications: Scheduling, statistical learning, game theory, and control.
Prerequisite
Instructor’s approval is required for crediting this course. Course requires a background in Markov processes.
Description
Modeling and analysis of a large system suffers from curse of dimensionality, since the state space grows exponentially with the system size. For an exchangeable system, an alternative approach to study such systems is via mean-field approach where one studies the evolution of empirical distribution of states across the system. In fact, the system can be easier to study in the large system limit. The aim of this course is to provide a systematic way to study such systems, providing conditions under which mean-field limits exist, and apply this study to problems in scheduling, statistical learning, game theory, and control.
Teams/GitHub/Overleaf Information
Teams
We will use Microsoft Teams for all the course related communication.
Please do not send any email regarding the course.
You can signup for the course team Mean-Field-2024 using the following code 7wzaupt.
GitHub
All the students in the class have read access to MeanField-Applications public repository on GitHub.
Please follow the guidelines in the sample lecture.
The source file for the sample lecture is in the repository.
It is recommended you save it with another name in your local repository for creating a new lecture.
Here is a good book for Git and a simple tutorial.
Overleaf
All the crediting students have access to the Overleaf project Mean-Field. Please follow the guidelines in the sampleLecture.tex, and save it with another name for creating a new lecture. Here is a good online resource to learn Overleaf.
Instructor
Parimal Parag
Office: EC 2.17
Hours: By appointment.
Time and Location
Classroom: EC 1.07, ECE main building
Hours: Tue/Thu 11:30am-01:00pm.
Teaching Assistants
TBD
Email: TBD
Hours: By appointment.
Grading Policy
Scribing: 50
Final Presentation: 50
References
Mean-field Interacting Particle Systems: Limit Laws and Large Deviations, Rajesh Sundaresan and Sarath Yasodharan, Tutorial slides, SIGMETRICS, 2022.
The Power of Two Choices in Randomized Load Balancing, Michael David Mitzenmacher, PhD Thesis, Harvard University, 1991.
Information, Physics, and Computation, Marc M'{e}zard and Andrea Montanari, Oxford University Press, 2009.
High-dimensional statistics: A non-asymptotic viewpoint, Martin Wainwright, Cambridge University Press, 2019.
Graphical Models Concepts in Compressed Sensing, Andrea Montanari, arXiv, 2011.
Mean field games and applications, Olivier Gu'{e}ant, Jean-Michel Lasry, Pierre-Louis Lions, Unpublished online book, 2023.