Approximating the Permanent with Fractional Belief Propagation The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Chertkov, Michael, and Adam B. Yedidia. “Approximating the Permanent with Fractional Belief Propagation.” Journal of Machine Learning Research 14 (2013): 2029–2066. As Published http://jmlr.org/papers/volume14/chertkov13a/chertkov13a.pdf Publisher Association for Computing Machinery (ACM) Version Final published version Citable link http://hdl.handle.net/1721.1/81423 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. JournalofMachineLearningResearch14(2013)2029-2066 Submitted 7/11; Revised 1/13; Published 7/13 Approximating the Permanent with Fractional Belief Propagation Michael Chertkov
[email protected] Theory Division & Center for Nonlinear Studies Los Alamos National Laboratory Los Alamos, NM 87545, USA Adam B. Yedidia∗
[email protected] Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139, USA Editor: Tony Jebara Abstract We discuss schemes for exact and approximate computations of permanents, and compare them with each other. Specifically, we analyze the belief propagation (BP) approach and its fractional belief propagation (FBP) generalization for computing the permanent of a non-negative matrix. Known bounds and Conjectures are verified in experiments, and some new theoretical relations, bounds and Conjectures are proposed. The fractional free energy (FFE) function is parameterized by a scalar parameter γ [ 1;1], where γ = 1 corresponds to the BP limit and γ = 1 corresponds to the exclusion principle∈ (but− ignoring perfect− matching constraints) mean-field (MF) limit.