--- _id: '3124' abstract: - lang: eng text: "We consider the problem of inference in a graphical model with binary variables. While in theory it is arguably preferable to compute marginal probabilities, in practice researchers often use MAP inference due to the availability of efficient discrete optimization algorithms. We bridge the gap between the two approaches by introducing the Discrete Marginals technique in which approximate marginals are obtained by minimizing an objective function with unary and pairwise terms over a discretized domain. This allows the use of techniques originally developed for MAP-MRF inference and learning. We explore two ways to set up the objective function - by discretizing the Bethe free energy and by learning it from training data. Experimental results show that for certain types of graphs a learned function can outperform the Bethe approximation. We also establish a link between the Bethe free energy and submodular functions.\r\n" alternative_title: - Inferning 2012 author: - first_name: Filip full_name: Korc, Filip id: 476A2FD6-F248-11E8-B48F-1D18A9856A87 last_name: Korc - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Korc F, Kolmogorov V, Lampert C. Approximating marginals using discrete energy minimization. In: ICML; 2012.' apa: 'Korc, F., Kolmogorov, V., & Lampert, C. (2012). Approximating marginals using discrete energy minimization. Presented at the ICML: International Conference on Machine Learning, Edinburgh, Scotland: ICML.' chicago: Korc, Filip, Vladimir Kolmogorov, and Christoph Lampert. “Approximating Marginals Using Discrete Energy Minimization.” ICML, 2012. ieee: 'F. Korc, V. Kolmogorov, and C. Lampert, “Approximating marginals using discrete energy minimization,” presented at the ICML: International Conference on Machine Learning, Edinburgh, Scotland, 2012.' ista: 'Korc F, Kolmogorov V, Lampert C. 2012. Approximating marginals using discrete energy minimization. ICML: International Conference on Machine Learning, Inferning 2012, .' mla: Korc, Filip, et al. Approximating Marginals Using Discrete Energy Minimization. ICML, 2012. short: F. Korc, V. Kolmogorov, C. Lampert, in:, ICML, 2012. conference: end_date: 2012-07-01 location: Edinburgh, Scotland name: 'ICML: International Conference on Machine Learning' start_date: 2012-06-26 date_created: 2018-12-11T12:01:31Z date_published: 2012-06-30T00:00:00Z date_updated: 2023-02-23T12:24:24Z day: '30' ddc: - '000' department: - _id: ChLa - _id: VlKo file: - access_level: open_access checksum: 3d0d4246548c736857302aadb2ff5d15 content_type: application/pdf creator: system date_created: 2018-12-12T10:11:34Z date_updated: 2020-07-14T12:46:00Z file_id: '4889' file_name: IST-2016-565-v1+1_DM-inferning2012.pdf file_size: 305836 relation: main_file file_date_updated: 2020-07-14T12:46:00Z has_accepted_license: '1' language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version publication_status: published publisher: ICML publist_id: '3575' pubrep_id: '565' quality_controlled: '1' related_material: record: - id: '5396' relation: later_version status: public status: public title: Approximating marginals using discrete energy minimization type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '5396' abstract: - lang: eng text: We consider the problem of inference in agraphical model with binary variables. While in theory it is arguably preferable to compute marginal probabilities, in practice researchers often use MAP inference due to the availability of efficient discrete optimization algorithms. We bridge the gap between the two approaches by introducing the Discrete Marginals technique in which approximate marginals are obtained by minimizing an objective function with unary and pair-wise terms over a discretized domain. This allows the use of techniques originally devel-oped for MAP-MRF inference and learning. We explore two ways to set up the objective function - by discretizing the Bethe free energy and by learning it from training data. Experimental results show that for certain types of graphs a learned function can out-perform the Bethe approximation. We also establish a link between the Bethe free energy and submodular functions. alternative_title: - IST Austria Technical Report author: - first_name: Filip full_name: Korc, Filip id: 476A2FD6-F248-11E8-B48F-1D18A9856A87 last_name: Korc - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: Korc F, Kolmogorov V, Lampert C. Approximating Marginals Using Discrete Energy Minimization. IST Austria; 2012. doi:10.15479/AT:IST-2012-0003 apa: Korc, F., Kolmogorov, V., & Lampert, C. (2012). Approximating marginals using discrete energy minimization. IST Austria. https://doi.org/10.15479/AT:IST-2012-0003 chicago: Korc, Filip, Vladimir Kolmogorov, and Christoph Lampert. Approximating Marginals Using Discrete Energy Minimization. IST Austria, 2012. https://doi.org/10.15479/AT:IST-2012-0003. ieee: F. Korc, V. Kolmogorov, and C. Lampert, Approximating marginals using discrete energy minimization. IST Austria, 2012. ista: Korc F, Kolmogorov V, Lampert C. 2012. Approximating marginals using discrete energy minimization, IST Austria, 13p. mla: Korc, Filip, et al. Approximating Marginals Using Discrete Energy Minimization. IST Austria, 2012, doi:10.15479/AT:IST-2012-0003. short: F. Korc, V. Kolmogorov, C. Lampert, Approximating Marginals Using Discrete Energy Minimization, IST Austria, 2012. date_created: 2018-12-12T11:39:06Z date_published: 2012-07-23T00:00:00Z date_updated: 2023-02-23T11:13:22Z day: '23' ddc: - '000' department: - _id: VlKo - _id: ChLa doi: 10.15479/AT:IST-2012-0003 file: - access_level: open_access checksum: 7e0ba85ad123b13223aaf6cdde2d288c content_type: application/pdf creator: system date_created: 2018-12-12T11:53:29Z date_updated: 2020-07-14T12:46:44Z file_id: '5490' file_name: IST-2012-0003_IST-2012-0003.pdf file_size: 618744 relation: main_file file_date_updated: 2020-07-14T12:46:44Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '13' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '36' related_material: record: - id: '3124' relation: earlier_version status: public status: public title: Approximating marginals using discrete energy minimization type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2012' ...