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Description

I will give an overview of some connections between statistical physics and Bayesian inference, which has allowed ideas from physics to be useful in solving problems from computer science. Imagine, for instance, the task of finding densely connected "communities" hidden in a random graph (network). The optimal method for inference is based on the posterior distribution, which is the Gibbs (or Boltzmann) distribution for some variant of the Ising model. The posterior distribution is not tractable to compute, but efficient algorithms have been developed to approximate it based on the Bethe or Kikuchi approximations to the free energy. The behavior of these methods reveals computational "phase transitions" akin to those in physics, where the difficulty of solving an inference problem changes abruptly as the signal-to-noise ratio crosses some threshold. Some related references include: - https://arxiv.org/abs/1803.11132 - https://arxiv.org/abs/1904.03858 - https://sphinxteam.github.io/EPFLDoctoralLecture2021/Notes.pdf