# 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} }

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

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#### References

SHOWING 1-8 OF 8 REFERENCES

Conditioning and covariance on caterpillars

- Mathematics, Computer Science
- 2015 IEEE Information Theory Workshop (ITW)
- 2015

4 Highly Influential- PDF

Gaussian-width gradient complexity, reverse log-Sobolev
inequalities and nonlinear large deviations

- Mathematics
- 2016

49 Highly Influential- PDF

Approximation schemes via Sherali-Adams hierarchy for dense constraint satisfaction problems and assignment problems

- Computer Science, Mathematics
- ITCS
- 2014

18 Highly Influential- PDF

Approximating CSPs with global cardinality constraints using SDP hierarchies

- Mathematics, Computer Science
- SODA
- 2012

61 Highly Influential- PDF

A Birthday Repetition Theorem and Complexity of Approximating Dense CSPs

- Mathematics, Computer Science
- ICALP
- 2017

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