---
_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. <i>Approximating Marginals Using Discrete Energy Minimization</i>.
    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:
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  - 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. <i>Approximating Marginals Using Discrete
    Energy Minimization</i>. IST Austria; 2012. doi:<a href="https://doi.org/10.15479/AT:IST-2012-0003">10.15479/AT:IST-2012-0003</a>
  apa: Korc, F., Kolmogorov, V., &#38; Lampert, C. (2012). <i>Approximating marginals
    using discrete energy minimization</i>. IST Austria. <a href="https://doi.org/10.15479/AT:IST-2012-0003">https://doi.org/10.15479/AT:IST-2012-0003</a>
  chicago: Korc, Filip, Vladimir Kolmogorov, and Christoph Lampert. <i>Approximating
    Marginals Using Discrete Energy Minimization</i>. IST Austria, 2012. <a href="https://doi.org/10.15479/AT:IST-2012-0003">https://doi.org/10.15479/AT:IST-2012-0003</a>.
  ieee: F. Korc, V. Kolmogorov, and C. Lampert, <i>Approximating marginals using discrete
    energy minimization</i>. 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. <i>Approximating Marginals Using Discrete Energy Minimization</i>.
    IST Austria, 2012, doi:<a href="https://doi.org/10.15479/AT:IST-2012-0003">10.15479/AT:IST-2012-0003</a>.
  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'
...