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The well known maximum-entropy principle due to Jaynes, which states thatgiven mean parameters, the maximum entropy distribution matching them is in anexponential family, has been very popular in machine learning due to its"Occam's razor" interpretation. Unfortunately, calculating the potentials inthe maximum-entropy distribution is intractable \cite{bresler2014hardness}. Weprovide computationally efficient versions of this principle when the meanparameters are pairwise moments: we design distributions that approximatelymatch given pairwise moments, while having entropy which is comparable to themaximum entropy distribution matching those moments.  We additionally provide surprising applications of the approximate maximumentropy principle to designing provable variational methods for partitionfunction calculations for Ising models without any assumptions on thepotentials of the model. More precisely, we show that in every temperature, wecan get approximation guarantees for the log-partition function comparable tothose in the low-temperature limit, which is the setting of optimization ofquadratic forms over the hypercube. \cite{alon2006approximating}

Approximate maximum entropy principles via Goemans-Williamson with applications to provable variational methods