{"type":"ScholarlyArticle","title":"Algorithms for Estimating the Partition Function of Restricted Boltzmann Machines (Extended Abstract)","authors":[{"name":"Oswin Krause","slug":"oswin-krause","given":"Oswin","family":"Krause","affiliation":"Department of Computer Science , University of Copenhagen , 2100 Copenhagen , Denmark"},{"name":"Asja Fischer","slug":"asja-fischer","given":"Asja","family":"Fischer","affiliation":"Faculty of Mathematics , Ruhr University Bochum , 44780 Bochum , Germany"},{"name":"Christian Igel","slug":"christian-igel","given":"Christian","family":"Igel","affiliation":"Department of Computer Science , University of Copenhagen , 2100 Copenhagen , Denmark"}],"abstract":"Estimating the normalization constants (partition functions) of energy-based probabilistic models (Markov random fields) with a high accuracy is required for measuring  performance, monitoring the training progress of adaptive models, and conducting likelihood ratio tests.   We devised a unifying theoretical framework for algorithms for estimating the partition function, including Annealed Importance Sampling (AIS) and Bennett's Acceptance Ratio method (BAR).  The unification reveals  conceptual similarities of and differences between  different approaches and suggests new algorithms. The framework is  based on a generalized form of Crooks' equality, which links the expectation over a distribution of samples generated by a transition operator to the expectation over the distribution induced by the reversed operator.  \r\nDifferent ways of sampling, such as parallel\r\ntempering and path sampling, are covered by the framework.  \r\nWe performed experiments in which we estimated the partition function of restricted Boltzmann\r\nmachines (RBMs) and Ising models. We found that BAR using parallel\r\ntempering worked well with a small number of bridging distributions,\r\nwhile path sampling based AIS performed best with many bridging\r\ndistributions.  The normalization constant is measured w.r.t.~a reference distribution, and the choice of this distribution turned out to be very important in our experiments.\r\nOverall, BAR gave the  best empirical results, outperforming AIS.","doi":"10.24963/ijcai.2020/704","url":"https://ijcai.org/proceedings/2020/704","pdf":"https://ijcai.org/proceedings/2020/0704.pdf","markdown":"https://ijcai.org/proceedings/2020/704.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/704","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Journal track","track":"Journal track","number":704,"pages":{"first":5045,"last":5049},"keywords":["Machine Learning: Learning Graphical Models","Machine Learning: Learning Generative Models"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25075/file_25075.m3u8","length_sec":216,"provider":"hls"}],"references":[{"position":1,"raw":"[Bennett, 1976] Charles H. 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