Student Probability Seminar Fall 2024
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Welcome to the Berkeley Student Probability Seminar, Fall 2024 edition! The broad topic for this semester is Approximation, inference and sampling of Gibbs measures. Since this is a highly interdisciplinary area, we wish to encourage talks from statistical and/or physical viewpoints, while also discussing aspects of interest to probabilists. Please see below for a short description and a couple of references to help us get started.

We take turns presenting, so please sign up! Google sheet for signing up.

Location and times: Evans 891, (almost) every Wednesday from 2 - 3 pm.

Please drop me (Mriganka) an email at mriganka_brc@berkeley.edu if there are any issues here, or if I forgot to update this website. For general queries, you may contact any one of the organizers:

Gibbs measures, a term we will generically use to refer to probability distributions described via exponentials of Hamiltonians, appear in extremely diverse contexts ranging from statistical physics, probability, statistical inference/ML, and more recently, in the theory of deep learning and generative models. These distributions are often high- (or infinite-) dimensional, and thereby exhibit a fascinating interaction between entropy aspects derived from the ambient space, and energy aspects derived from the defining Hamiltonian. Since this Hamiltonian may include nonlinear interactions, for instance in spin glasses, the so-called "energy landscape" is often highly complex. Due to this intractable nature, various approximation and sampling techniques have been devised over the years, such as, MCMC techniques, mean-field approximations, message-passing heuristics, variational inference and score modelling to name a few. Viewed as a whole, the field represents one of the most important and far-reaching topics of modern research, borrowing ideas from and contributing back to an ever-growing range of disciplines. The purpose of this seminar would be to broadly visit some of these aspects, as well as to discuss various tools, both rigorous and non-rigorous, employed to dissect these objects.

References (please feel free to suggest more!):

  1. Gibbs measures on lattices from a rigorous, statistical-physics viewpoint: https://www.unige.ch/math/folks/velenik/smbook/
  2. Low-complexity Gibbs measures: https://arxiv.org/abs/1810.07278, https://arxiv.org/pdf/1612.04346
  3. A collection of lectures and useful references to the stochastic localization/sampling literature: https://metaphor.ethz.ch/x/2024/fs/401-4634-24L/
  4. A broad survey on the "physics" approach to statistical problems: https://arxiv.org/pdf/1511.02476
  5. A more book-style presentation of these topics: https://sphinxteam.github.io/EPFLDoctoralLecture2021/Notes.pdf
  6. A short collection of lectures describing tools from physics and their applications to statistical problems: https://brloureiro.github.io/assets/pdf/NotesPrinceton_BL.pdf
  7. A book on graphical models and their inference: https://www.cs.columbia.edu/~blei/fogm/2023F/readings/WainwrightJordan2008.pdf
  8. A survey on variational inference, and some intuitive and algorithmic aspects: https://arxiv.org/pdf/1601.00670
  9. Energy-based models: https://arxiv.org/pdf/2101.03288, a tutorial: https://energy-based-models.github.io/ijcai2022-tutorial
  10. A tutorial on normalizing flows: https://www.youtube.com/watch?v=7TOvhz93G9o
  11. A tutorial on diffusion models: https://arxiv.org/pdf/2208.11970
Date Speaker Summary
Oct 02 Mriganka Basu Roy Chowdhury

Mean-field approximations for log-concave distributions. [LMY24], [Notes].

Sep 25 David X. Wu

MaxCut and MaxBisection on random \(d\)-regular graphs. [Dembo, Montanari, Sen, 2015]

Sep 18 Karissa Huang

Bernoulli percolation, phase transitions and criticality in \(\Z^2\).

Sep 11 Michael Kielstra

Pseudofermion Fields in Gaussian Process Settings, Or, How to Sample with Determinants Without Going Stark Raving Mad

Sep 04 Vilas Sreenivasan Winstein

An introduction to approximation, inference and sampling of Gibbs measures. [Notes]