---
_id: '274'
abstract:
- lang: eng
text: 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.
article_processing_charge: No
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: '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.'
apa: 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.
chicago: 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.
ieee: 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.
ista: '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.'
mla: 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.
short: V. Kolmogorov, in:, Proceedings of the 31st Conference On Learning Theory,
PMLR, 2017, pp. 228–249.
conference:
end_date: 2018-07-09
name: 'COLT: Annual Conference on Learning Theory '
start_date: 2018-07-06
date_created: 2018-12-11T11:45:33Z
date_published: 2017-12-27T00:00:00Z
date_updated: 2021-01-12T06:59:23Z
day: '27'
ddc:
- '510'
department:
- _id: VlKo
ec_funded: 1
external_id:
arxiv:
- '1608.04223'
file:
- access_level: open_access
checksum: 89db06a0e8083524449cb59b56bf4e5b
content_type: application/pdf
creator: dernst
date_created: 2020-05-12T09:23:27Z
date_updated: 2020-07-14T12:45:45Z
file_id: '7820'
file_name: 2018_PMLR_Kolmogorov.pdf
file_size: 408974
relation: main_file
file_date_updated: 2020-07-14T12:45:45Z
has_accepted_license: '1'
intvolume: ' 75'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 228-249
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Proceedings of the 31st Conference On Learning Theory
publication_status: published
publisher: PMLR
publist_id: '7628'
quality_controlled: '1'
status: public
title: A faster approximation algorithm for the Gibbs partition function
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 75
year: '2017'
...