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Course

PHYS-642: Statistical physics for optimization & learning

Lectures in this course (44)

Covers linear problems, LASSO, and AMP in supervised learning, including Generalized Linear Models and N-dimensional models.

Explores the cavity method, Approximate Message Passing, and phase transitions in probabilistic models.

Covers statistical physics tools for optimization, learning, graph coloring, recommendation systems, and neural networks.

Explores the relationship between colors and condensation in clustering algorithms.

Explores optimal Bayesian inference, denoising, scalar estimation, and phase transitions.

Explores Replica Symmetry Breaking in the Random Energy Model, focusing on configurations, variance, mean, and system behavior.

Introduces Julia for computational physics, focusing on simulation methods and efficiency optimizations.

Delves into large deviations in statistical mechanics, exploring Kramer's theorem, Varadhan's lemma, and Laplace's method.

Provides an in-depth analysis of the Random Field Ising Model, covering model description, free entropy, and mean field algorithm.

Covers random matrix theory and the replica method to compute quantities related to non-hermitic series using the Stieltjes transform.

Explores the Random Field Ising Model on random graphs, discussing belief propagation updates and population dynamics.

Discusses the Potts model on random graphs, belief propagation, and simplifying messages.

Explores the p-spin model in spin glass theory and the convergence to the Random Energy Model using Gaussian integrals and the replica method.

Explores the computation of the replica for the p-spin model, focusing on decoupling and recoupling replicas to simplify calculations.

Explores the Survey Propagation algorithm and its application in solving constraint satisfaction problems.

Covers the basics of information theory and its applications in various fields.

Explores the Curie-Weiss model, spin glasses, and optimization problems in statistical physics.

Explores the Spike-Wigner model, low-rank matrix factorization, and Gaussian matrices.

Covers the replica method for computing expectations and the heuristic evaluation of expressions.

Explores deep learning fundamentals, including image classification, neural network working principles, and machine learning challenges.