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:
See abstract for more details on the topic and some references.
Abstract
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!):
- Gibbs measures on lattices from a rigorous, statistical-physics viewpoint: book
- Low-complexity Gibbs measures: paper-1, paper-2
- A collection of lectures and useful references to the stochastic localization/sampling literature: link
- A broad survey on the "physics" approach to statistical problems: survey
- A more book-style presentation of these topics: book
- A short collection of lectures describing tools from physics and their applications to statistical problems: lecture notes
- A book on graphical models and their inference: book
- A survey on variational inference, and some intuitive and algorithmic aspects: survey
- Energy-based models: paper, tutorial
- A tutorial on normalizing flows: link
- A tutorial on diffusion models: link