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

@article{Jain2019MeanfieldAC,
  title={Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective},
  author={V. Jain and F. Koehler and Andrej Risteski},
  journal={Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing},
  year={2019}
}
  • V. Jain, F. Koehler, Andrej Risteski
  • Published 2019
  • Computer Science, Mathematics
  • 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… CONTINUE READING
    12 Citations

    References

    SHOWING 1-8 OF 8 REFERENCES
    Universality of the mean-field for the Potts model
    • 35
    • Highly Influential
    • PDF
    Conditioning and covariance on caterpillars
    • 4
    • Highly Influential
    • PDF
    Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations
    • 49
    • Highly Influential
    • PDF
    Approximation schemes via Sherali-Adams hierarchy for dense constraint satisfaction problems and assignment problems
    • 18
    • Highly Influential
    • PDF
    Approximating CSPs with global cardinality constraints using SDP hierarchies
    • 61
    • Highly Influential
    • PDF
    A Birthday Repetition Theorem and Complexity of Approximating Dense CSPs
    • 62
    • Highly Influential
    • PDF
    Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective
    • 2018
    2014]: missing sign terms in the relation between C(XS) and I(XS)
    • 2014