{"day":"01","article_number":"72","has_accepted_license":"1","article_processing_charge":"Yes","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","doi":"10.4230/LIPIcs.ICALP.2023.72","file":[{"checksum":"6dee0684245bb1c524b9c955db1e933d","relation":"main_file","access_level":"open_access","success":1,"file_name":"2023_LIPIcsICALP_Harris.pdf","content_type":"application/pdf","file_id":"14088","date_created":"2023-08-21T06:45:16Z","file_size":917791,"date_updated":"2023-08-21T06:45:16Z","creator":"dernst"}],"file_date_updated":"2023-08-21T06:45:16Z","abstract":[{"lang":"eng","text":"A central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We will consider sampling problems which come from Gibbs distributions, which are families of probability distributions over a discrete space Ω with probability mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max] and H(ω) ∈ {0} ∪ [1, n].\r\nThe partition function is the normalization factor Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the log partition ratio is defined as q = (log Z(β_max))/Z(β_min)\r\nWe develop a number of algorithms to estimate the counts c_x using roughly Õ(q/ε²) samples for general Gibbs distributions and Õ(n²/ε²) samples for integer-valued distributions (ignoring some second-order terms and parameters), We show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs and perfect matchings in a graph."}],"acknowledgement":"We thank Heng Guo for helpful explanations of algorithms for sampling connected subgraphs and matchings, Maksym Serbyn for bringing to our attention the Wang-Landau algorithm and its use in physics.","date_created":"2023-08-20T22:01:14Z","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959772785"],"issn":["1868-8969"]},"intvolume":"       261","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"author":[{"first_name":"David G.","last_name":"Harris","full_name":"Harris, David G."},{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir"}],"type":"conference","publication_status":"published","quality_controlled":"1","alternative_title":["LIPIcs"],"date_updated":"2023-08-21T06:49:11Z","date_published":"2023-07-01T00:00:00Z","ddc":["000","510"],"volume":261,"year":"2023","scopus_import":"1","oa_version":"Published Version","status":"public","conference":{"start_date":"2023-07-10","name":"ICALP: International Colloquium on Automata, Languages, and Programming","location":"Paderborn, Germany","end_date":"2023-07-14"},"publication":"50th International Colloquium on Automata, Languages, and Programming","department":[{"_id":"VlKo"}],"external_id":{"arxiv":["2007.10824"]},"title":"Parameter estimation for Gibbs distributions","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” In <i>50th International Colloquium on Automata, Languages, and Programming</i>, Vol. 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.72\">https://doi.org/10.4230/LIPIcs.ICALP.2023.72</a>.","short":"D.G. Harris, V. Kolmogorov, in:, 50th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","ama":"Harris DG, Kolmogorov V. Parameter estimation for Gibbs distributions. In: <i>50th International Colloquium on Automata, Languages, and Programming</i>. Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.72\">10.4230/LIPIcs.ICALP.2023.72</a>","ieee":"D. G. Harris and V. Kolmogorov, “Parameter estimation for Gibbs distributions,” in <i>50th International Colloquium on Automata, Languages, and Programming</i>, Paderborn, Germany, 2023, vol. 261.","ista":"Harris DG, Kolmogorov V. 2023. Parameter estimation for Gibbs distributions. 50th International Colloquium on Automata, Languages, and Programming. ICALP: International Colloquium on Automata, Languages, and Programming, LIPIcs, vol. 261, 72.","mla":"Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” <i>50th International Colloquium on Automata, Languages, and Programming</i>, vol. 261, 72, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.72\">10.4230/LIPIcs.ICALP.2023.72</a>.","apa":"Harris, D. G., &#38; Kolmogorov, V. (2023). Parameter estimation for Gibbs distributions. In <i>50th International Colloquium on Automata, Languages, and Programming</i> (Vol. 261). Paderborn, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.72\">https://doi.org/10.4230/LIPIcs.ICALP.2023.72</a>"},"_id":"14084","month":"07"}