Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective

  title={Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective},
  author={Vishesh Jain and Frederic Koehler and Andrej Risteski},
  journal={Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing},
The free energy is a key quantity of interest in Ising models, but unfortunately, computing it in general is computationally intractable. Two popular (variational) approximation schemes for estimating the free energy of general Ising models (in particular, even in regimes where correlation decay does not hold) are: (i) the mean-field approximation with roots in statistical physics, which estimates the free energy from below, and (ii) hierarchies of convex relaxations with roots in theoretical… 

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