A faster approximation algorithm for the Gibbs partition function

V. Kolmogorov, in:, Proceedings of the 31st Conference On Learning Theory, PMLR, 2017, pp. 228–249.

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Abstract
We consider the problem of estimating the partition function Z(β)=∑xexp(−β(H(x)) of a Gibbs distribution with a Hamilton H(⋅), or more precisely the logarithm of the ratio q=lnZ(0)/Z(β). It has been recently shown how to approximate q with high probability assuming the existence of an oracle that produces samples from the Gibbs distribution for a given parameter value in [0,β]. The current best known approach due to Huber [9] uses O(qlnn⋅[lnq+lnlnn+ε−2]) oracle calls on average where ε is the desired accuracy of approximation and H(⋅) is assumed to lie in {0}∪[1,n]. We improve the complexity to O(qlnn⋅ε−2) oracle calls. We also show that the same complexity can be achieved if exact oracles are replaced with approximate sampling oracles that are within O(ε2qlnn) variation distance from exact oracles. Finally, we prove a lower bound of Ω(q⋅ε−2) oracle calls under a natural model of computation.
Publishing Year
Date Published
2017-12-27
Proceedings Title
Proceedings of the 31st Conference On Learning Theory
Volume
75
Page
228-249
Conference
COLT: Annual Conference on Learning Theory
Conference Date
2018-07-06 – 2018-07-09
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Cite this

Kolmogorov V. A faster approximation algorithm for the Gibbs partition function. In: Proceedings of the 31st Conference On Learning Theory. Vol 75. PMLR; 2017:228-249.
Kolmogorov, V. (2017). A faster approximation algorithm for the Gibbs partition function. In Proceedings of the 31st Conference On Learning Theory (Vol. 75, pp. 228–249). PMLR.
Kolmogorov, Vladimir. “A Faster Approximation Algorithm for the Gibbs Partition Function.” In Proceedings of the 31st Conference On Learning Theory, 75:228–49. PMLR, 2017.
V. Kolmogorov, “A faster approximation algorithm for the Gibbs partition function,” in Proceedings of the 31st Conference On Learning Theory, 2017, vol. 75, pp. 228–249.
Kolmogorov V. 2017. A faster approximation algorithm for the Gibbs partition function. Proceedings of the 31st Conference On Learning Theory. COLT: Annual Conference on Learning Theory vol. 75. 228–249.
Kolmogorov, Vladimir. “A Faster Approximation Algorithm for the Gibbs Partition Function.” Proceedings of the 31st Conference On Learning Theory, vol. 75, PMLR, 2017, pp. 228–49.
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