---
_id: '641'
abstract:
- lang: eng
text: 'We introduce two novel methods for learning parameters of graphical models
for image labelling. The following two tasks underline both methods: (i) perturb
model parameters based on given features and ground truth labelings, so as to
exactly reproduce these labelings as optima of the local polytope relaxation of
the labelling problem; (ii) train a predictor for the perturbed model parameters
so that improved model parameters can be applied to the labelling of novel data.
Our first method implements task (i) by inverse linear programming and task (ii)
using a regressor e.g. a Gaussian process. Our second approach simultaneously
solves tasks (i) and (ii) in a joint manner, while being restricted to linearly
parameterised predictors. Experiments demonstrate the merits of both approaches.'
alternative_title:
- LNCS
author:
- first_name: Vera
full_name: Trajkovska, Vera
last_name: Trajkovska
- first_name: Paul
full_name: Swoboda, Paul
id: 446560C6-F248-11E8-B48F-1D18A9856A87
last_name: Swoboda
- first_name: Freddie
full_name: Åström, Freddie
last_name: Åström
- first_name: Stefanie
full_name: Petra, Stefanie
last_name: Petra
citation:
ama: 'Trajkovska V, Swoboda P, Åström F, Petra S. Graphical model parameter learning
by inverse linear programming. In: Lauze F, Dong Y, Bjorholm Dahl A, eds. Vol
10302. Springer; 2017:323-334. doi:10.1007/978-3-319-58771-4_26'
apa: 'Trajkovska, V., Swoboda, P., Åström, F., & Petra, S. (2017). Graphical
model parameter learning by inverse linear programming. In F. Lauze, Y. Dong,
& A. Bjorholm Dahl (Eds.) (Vol. 10302, pp. 323–334). Presented at the SSVM:
Scale Space and Variational Methods in Computer Vision, Kolding, Denmark: Springer.
https://doi.org/10.1007/978-3-319-58771-4_26'
chicago: Trajkovska, Vera, Paul Swoboda, Freddie Åström, and Stefanie Petra. “Graphical
Model Parameter Learning by Inverse Linear Programming.” edited by François Lauze,
Yiqiu Dong, and Anders Bjorholm Dahl, 10302:323–34. Springer, 2017. https://doi.org/10.1007/978-3-319-58771-4_26.
ieee: 'V. Trajkovska, P. Swoboda, F. Åström, and S. Petra, “Graphical model parameter
learning by inverse linear programming,” presented at the SSVM: Scale Space and
Variational Methods in Computer Vision, Kolding, Denmark, 2017, vol. 10302, pp.
323–334.'
ista: 'Trajkovska V, Swoboda P, Åström F, Petra S. 2017. Graphical model parameter
learning by inverse linear programming. SSVM: Scale Space and Variational Methods
in Computer Vision, LNCS, vol. 10302, 323–334.'
mla: Trajkovska, Vera, et al. Graphical Model Parameter Learning by Inverse Linear
Programming. Edited by François Lauze et al., vol. 10302, Springer, 2017,
pp. 323–34, doi:10.1007/978-3-319-58771-4_26.
short: V. Trajkovska, P. Swoboda, F. Åström, S. Petra, in:, F. Lauze, Y. Dong, A.
Bjorholm Dahl (Eds.), Springer, 2017, pp. 323–334.
conference:
end_date: 2017-06-08
location: Kolding, Denmark
name: 'SSVM: Scale Space and Variational Methods in Computer Vision'
start_date: 2017-06-04
date_created: 2018-12-11T11:47:39Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:07:23Z
day: '01'
department:
- _id: VlKo
doi: 10.1007/978-3-319-58771-4_26
editor:
- first_name: François
full_name: Lauze, François
last_name: Lauze
- first_name: Yiqiu
full_name: Dong, Yiqiu
last_name: Dong
- first_name: Anders
full_name: Bjorholm Dahl, Anders
last_name: Bjorholm Dahl
intvolume: ' 10302'
language:
- iso: eng
month: '01'
oa_version: None
page: 323 - 334
publication_identifier:
isbn:
- 978-331958770-7
publication_status: published
publisher: Springer
publist_id: '7147'
quality_controlled: '1'
scopus_import: 1
status: public
title: Graphical model parameter learning by inverse linear programming
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 10302
year: '2017'
...
---
_id: '644'
abstract:
- lang: eng
text: An instance of the valued constraint satisfaction problem (VCSP) is given
by a finite set of variables, a finite domain of labels, and a sum of functions,
each function depending on a subset of the variables. Each function can take finite
values specifying costs of assignments of labels to its variables or the infinite
value, which indicates an infeasible assignment. The goal is to find an assignment
of labels to the variables that minimizes the sum. We study, assuming that P 6=
NP, how the complexity of this very general problem depends on the set of functions
allowed in the instances, the so-called constraint language. The case when all
allowed functions take values in f0;1g corresponds to ordinary CSPs, where one
deals only with the feasibility issue, and there is no optimization. This case
is the subject of the algebraic CSP dichotomy conjecture predicting for which
constraint languages CSPs are tractable (i.e., solvable in polynomial time) and
for which they are NP-hard. The case when all allowed functions take only finite
values corresponds to a finitevalued CSP, where the feasibility aspect is trivial
and one deals only with the optimization issue. The complexity of finite-valued
CSPs was fully classified by Thapper and Živný. An algebraic necessary condition
for tractability of a general-valued CSP with a fixed constraint language was
recently given by Kozik and Ochremiak. As our main result, we prove that if a
constraint language satisfies this algebraic necessary condition, and the feasibility
CSP (i.e., the problem of deciding whether a given instance has a feasible solution)
corresponding to the VCSP with this language is tractable, then the VCSP is tractable.
The algorithm is a simple combination of the assumed algorithm for the feasibility
CSP and the standard LP relaxation. As a corollary, we obtain that a dichotomy
for ordinary CSPs would imply a dichotomy for general-valued CSPs.
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Andrei
full_name: Krokhin, Andrei
last_name: Krokhin
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: Kolmogorov V, Krokhin A, Rolinek M. The complexity of general-valued CSPs.
SIAM Journal on Computing. 2017;46(3):1087-1110. doi:10.1137/16M1091836
apa: Kolmogorov, V., Krokhin, A., & Rolinek, M. (2017). The complexity of general-valued
CSPs. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/16M1091836
chicago: Kolmogorov, Vladimir, Andrei Krokhin, and Michal Rolinek. “The Complexity
of General-Valued CSPs.” SIAM Journal on Computing. SIAM, 2017. https://doi.org/10.1137/16M1091836.
ieee: V. Kolmogorov, A. Krokhin, and M. Rolinek, “The complexity of general-valued
CSPs,” SIAM Journal on Computing, vol. 46, no. 3. SIAM, pp. 1087–1110,
2017.
ista: Kolmogorov V, Krokhin A, Rolinek M. 2017. The complexity of general-valued
CSPs. SIAM Journal on Computing. 46(3), 1087–1110.
mla: Kolmogorov, Vladimir, et al. “The Complexity of General-Valued CSPs.” SIAM
Journal on Computing, vol. 46, no. 3, SIAM, 2017, pp. 1087–110, doi:10.1137/16M1091836.
short: V. Kolmogorov, A. Krokhin, M. Rolinek, SIAM Journal on Computing 46 (2017)
1087–1110.
date_created: 2018-12-11T11:47:40Z
date_published: 2017-06-29T00:00:00Z
date_updated: 2023-02-23T10:07:49Z
day: '29'
department:
- _id: VlKo
doi: 10.1137/16M1091836
ec_funded: 1
intvolume: ' 46'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1502.07327
month: '06'
oa: 1
oa_version: Preprint
page: 1087 - 1110
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: SIAM Journal on Computing
publication_status: published
publisher: SIAM
publist_id: '7138'
quality_controlled: '1'
related_material:
record:
- id: '1637'
relation: other
status: public
scopus_import: 1
status: public
title: The complexity of general-valued CSPs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 46
year: '2017'
...
---
_id: '646'
abstract:
- lang: eng
text: We present a novel convex relaxation and a corresponding inference algorithm
for the non-binary discrete tomography problem, that is, reconstructing discrete-valued
images from few linear measurements. In contrast to state of the art approaches
that split the problem into a continuous reconstruction problem for the linear
measurement constraints and a discrete labeling problem to enforce discrete-valued
reconstructions, we propose a joint formulation that addresses both problems simultaneously,
resulting in a tighter convex relaxation. For this purpose a constrained graphical
model is set up and evaluated using a novel relaxation optimized by dual decomposition.
We evaluate our approach experimentally and show superior solutions both mathematically
(tighter relaxation) and experimentally in comparison to previously proposed relaxations.
alternative_title:
- LNCS
author:
- first_name: Jan
full_name: Kuske, Jan
last_name: Kuske
- first_name: Paul
full_name: Swoboda, Paul
id: 446560C6-F248-11E8-B48F-1D18A9856A87
last_name: Swoboda
- first_name: Stefanie
full_name: Petra, Stefanie
last_name: Petra
citation:
ama: 'Kuske J, Swoboda P, Petra S. A novel convex relaxation for non binary discrete
tomography. In: Lauze F, Dong Y, Bjorholm Dahl A, eds. Vol 10302. Springer; 2017:235-246.
doi:10.1007/978-3-319-58771-4_19'
apa: 'Kuske, J., Swoboda, P., & Petra, S. (2017). A novel convex relaxation
for non binary discrete tomography. In F. Lauze, Y. Dong, & A. Bjorholm Dahl
(Eds.) (Vol. 10302, pp. 235–246). Presented at the SSVM: Scale Space and Variational
Methods in Computer Vision, Kolding, Denmark: Springer. https://doi.org/10.1007/978-3-319-58771-4_19'
chicago: Kuske, Jan, Paul Swoboda, and Stefanie Petra. “A Novel Convex Relaxation
for Non Binary Discrete Tomography.” edited by François Lauze, Yiqiu Dong, and
Anders Bjorholm Dahl, 10302:235–46. Springer, 2017. https://doi.org/10.1007/978-3-319-58771-4_19.
ieee: 'J. Kuske, P. Swoboda, and S. Petra, “A novel convex relaxation for non binary
discrete tomography,” presented at the SSVM: Scale Space and Variational Methods
in Computer Vision, Kolding, Denmark, 2017, vol. 10302, pp. 235–246.'
ista: 'Kuske J, Swoboda P, Petra S. 2017. A novel convex relaxation for non binary
discrete tomography. SSVM: Scale Space and Variational Methods in Computer Vision,
LNCS, vol. 10302, 235–246.'
mla: Kuske, Jan, et al. A Novel Convex Relaxation for Non Binary Discrete Tomography.
Edited by François Lauze et al., vol. 10302, Springer, 2017, pp. 235–46, doi:10.1007/978-3-319-58771-4_19.
short: J. Kuske, P. Swoboda, S. Petra, in:, F. Lauze, Y. Dong, A. Bjorholm Dahl
(Eds.), Springer, 2017, pp. 235–246.
conference:
end_date: 2017-06-08
location: Kolding, Denmark
name: 'SSVM: Scale Space and Variational Methods in Computer Vision'
start_date: 2017-06-04
date_created: 2018-12-11T11:47:41Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2021-01-12T08:07:34Z
day: '01'
department:
- _id: VlKo
doi: 10.1007/978-3-319-58771-4_19
ec_funded: 1
editor:
- first_name: François
full_name: Lauze, François
last_name: Lauze
- first_name: Yiqiu
full_name: Dong, Yiqiu
last_name: Dong
- first_name: Anders
full_name: Bjorholm Dahl, Anders
last_name: Bjorholm Dahl
intvolume: ' 10302'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1703.03769
month: '06'
oa: 1
oa_version: Submitted Version
page: 235 - 246
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication_identifier:
isbn:
- 978-331958770-7
publication_status: published
publisher: Springer
publist_id: '7132'
quality_controlled: '1'
scopus_import: 1
status: public
title: A novel convex relaxation for non binary discrete tomography
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 10302
year: '2017'
...
---
_id: '992'
abstract:
- lang: eng
text: "An instance of the Constraint Satisfaction Problem (CSP) is given by a finite
set of\r\nvariables, a finite domain of labels, and a set of constraints, each
constraint acting on\r\na subset of the variables. The goal is to find an assignment
of labels to its variables\r\nthat satisfies all constraints (or decide whether
one exists). If we allow more general\r\n“soft” constraints, which come with (possibly
infinite) costs of particular assignments,\r\nwe obtain instances from a richer
class called Valued Constraint Satisfaction Problem\r\n(VCSP). There the goal
is to find an assignment with minimum total cost.\r\nIn this thesis, we focus
(assuming that P\r\n6\r\n=\r\nNP) on classifying computational com-\r\nplexity
of CSPs and VCSPs under certain restricting conditions. Two results are the core\r\ncontent
of the work. In one of them, we consider VCSPs parametrized by a constraint\r\nlanguage,
that is the set of “soft” constraints allowed to form the instances, and finish\r\nthe
complexity classification modulo (missing pieces of) complexity classification
for\r\nanalogously parametrized CSP. The other result is a generalization of Edmonds’
perfect\r\nmatching algorithm. This generalization contributes to complexity classfications
in two\r\nways. First, it gives a new (largest known) polynomial-time solvable
class of Boolean\r\nCSPs in which every variable may appear in at most two constraints
and second, it\r\nsettles full classification of Boolean CSPs with planar drawing
(again parametrized by a\r\nconstraint language)."
acknowledgement: FP7/2007-2013/ERC grant agreement no 616160
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: Rolinek M. Complexity of constraint satisfaction. 2017. doi:10.15479/AT:ISTA:th_815
apa: Rolinek, M. (2017). Complexity of constraint satisfaction. Institute
of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_815
chicago: Rolinek, Michal. “Complexity of Constraint Satisfaction.” Institute of
Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_815.
ieee: M. Rolinek, “Complexity of constraint satisfaction,” Institute of Science
and Technology Austria, 2017.
ista: Rolinek M. 2017. Complexity of constraint satisfaction. Institute of Science
and Technology Austria.
mla: Rolinek, Michal. Complexity of Constraint Satisfaction. Institute of
Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_815.
short: M. Rolinek, Complexity of Constraint Satisfaction, Institute of Science and
Technology Austria, 2017.
date_created: 2018-12-11T11:49:35Z
date_published: 2017-05-01T00:00:00Z
date_updated: 2023-09-07T12:05:41Z
day: '01'
ddc:
- '004'
degree_awarded: PhD
department:
- _id: VlKo
doi: 10.15479/AT:ISTA:th_815
ec_funded: 1
file:
- access_level: open_access
checksum: 81761fb939acb7585c36629f765b4373
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creator: system
date_created: 2018-12-12T10:07:55Z
date_updated: 2020-07-14T12:48:18Z
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content_type: application/zip
creator: dernst
date_created: 2019-04-05T08:43:24Z
date_updated: 2020-07-14T12:48:18Z
file_id: '6208'
file_name: 2017_Thesis_Rolinek_source.zip
file_size: 5936337
relation: source_file
file_date_updated: 2020-07-14T12:48:18Z
has_accepted_license: '1'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: '97'
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '6407'
pubrep_id: '815'
status: public
supervisor:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
title: Complexity of constraint satisfaction
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2017'
...
---
_id: '1192'
abstract:
- lang: eng
text: The main result of this paper is a generalization of the classical blossom
algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean
CSPs where each variable appears in exactly two constraints (we call it edge CSP)
and all constraints are even Δ-matroid relations (represented by lists of tuples).
As a consequence of this, we settle the complexity classification of planar Boolean
CSPs started by Dvorak and Kupec. Knowing that edge CSP is tractable for even
Δ-matroid constraints allows us to extend the tractability result to a larger
class of Δ-matroids that includes many classes that were known to be tractable
before, namely co-independent, compact, local and binary.
article_processing_charge: No
author:
- first_name: Alexandr
full_name: Kazda, Alexandr
id: 3B32BAA8-F248-11E8-B48F-1D18A9856A87
last_name: Kazda
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: 'Kazda A, Kolmogorov V, Rolinek M. Even delta-matroids and the complexity of
planar Boolean CSPs. In: SIAM; 2017:307-326. doi:10.1137/1.9781611974782.20'
apa: 'Kazda, A., Kolmogorov, V., & Rolinek, M. (2017). Even delta-matroids and
the complexity of planar Boolean CSPs (pp. 307–326). Presented at the SODA: Symposium
on Discrete Algorithms, Barcelona, Spain: SIAM. https://doi.org/10.1137/1.9781611974782.20'
chicago: Kazda, Alexandr, Vladimir Kolmogorov, and Michal Rolinek. “Even Delta-Matroids
and the Complexity of Planar Boolean CSPs,” 307–26. SIAM, 2017. https://doi.org/10.1137/1.9781611974782.20.
ieee: 'A. Kazda, V. Kolmogorov, and M. Rolinek, “Even delta-matroids and the complexity
of planar Boolean CSPs,” presented at the SODA: Symposium on Discrete Algorithms,
Barcelona, Spain, 2017, pp. 307–326.'
ista: 'Kazda A, Kolmogorov V, Rolinek M. 2017. Even delta-matroids and the complexity
of planar Boolean CSPs. SODA: Symposium on Discrete Algorithms, 307–326.'
mla: Kazda, Alexandr, et al. Even Delta-Matroids and the Complexity of Planar
Boolean CSPs. SIAM, 2017, pp. 307–26, doi:10.1137/1.9781611974782.20.
short: A. Kazda, V. Kolmogorov, M. Rolinek, in:, SIAM, 2017, pp. 307–326.
conference:
end_date: 2017-01019
location: Barcelona, Spain
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2017-01-16
date_created: 2018-12-11T11:50:38Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-09-20T11:20:26Z
day: '01'
department:
- _id: VlKo
doi: 10.1137/1.9781611974782.20
ec_funded: 1
external_id:
isi:
- '000426965800020'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1602.03124
month: '01'
oa: 1
oa_version: Submitted Version
page: 307 - 326
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication_identifier:
isbn:
- 978-161197478-2
publication_status: published
publisher: SIAM
publist_id: '6159'
quality_controlled: '1'
related_material:
record:
- id: '6032'
relation: later_version
status: public
status: public
title: Even delta-matroids and the complexity of planar Boolean CSPs
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2017'
...