Convex Relaxations for Learning Bounded-Treewidth Decomposable Graphs

K. S. Sesh Kumar, Francis Bach
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(1):525-533, 2013.

Abstract

We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this paper, we pose it as a combinatorial optimization problem, which is then relaxed to a convex optimization problem that involves searching over the forest and hyperforest polytopes with special structures. A supergradient method is used to solve the dual problem, with a run-time complexity of O(k^3 n^k+2 \log n) for each iteration, where n is the number of variables and k is a bound on the treewidth. We compare our approach to state-of-the-art methods on synthetic datasets and classical benchmarks, showing the gains of the novel convex approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-kumar13c, title = {Convex Relaxations for Learning Bounded-Treewidth Decomposable Graphs}, author = {Kumar, K. S. Sesh and Bach, Francis}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {525--533}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {1}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/kumar13c.pdf}, url = {https://proceedings.mlr.press/v28/kumar13c.html}, abstract = {We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this paper, we pose it as a combinatorial optimization problem, which is then relaxed to a convex optimization problem that involves searching over the forest and hyperforest polytopes with special structures. A supergradient method is used to solve the dual problem, with a run-time complexity of O(k^3 n^k+2 \log n) for each iteration, where n is the number of variables and k is a bound on the treewidth. We compare our approach to state-of-the-art methods on synthetic datasets and classical benchmarks, showing the gains of the novel convex approach.} }
Endnote
%0 Conference Paper %T Convex Relaxations for Learning Bounded-Treewidth Decomposable Graphs %A K. S. Sesh Kumar %A Francis Bach %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-kumar13c %I PMLR %P 525--533 %U https://proceedings.mlr.press/v28/kumar13c.html %V 28 %N 1 %X We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this paper, we pose it as a combinatorial optimization problem, which is then relaxed to a convex optimization problem that involves searching over the forest and hyperforest polytopes with special structures. A supergradient method is used to solve the dual problem, with a run-time complexity of O(k^3 n^k+2 \log n) for each iteration, where n is the number of variables and k is a bound on the treewidth. We compare our approach to state-of-the-art methods on synthetic datasets and classical benchmarks, showing the gains of the novel convex approach.
RIS
TY - CPAPER TI - Convex Relaxations for Learning Bounded-Treewidth Decomposable Graphs AU - K. S. Sesh Kumar AU - Francis Bach BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/02/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-kumar13c PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 1 SP - 525 EP - 533 L1 - http://proceedings.mlr.press/v28/kumar13c.pdf UR - https://proceedings.mlr.press/v28/kumar13c.html AB - We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this paper, we pose it as a combinatorial optimization problem, which is then relaxed to a convex optimization problem that involves searching over the forest and hyperforest polytopes with special structures. A supergradient method is used to solve the dual problem, with a run-time complexity of O(k^3 n^k+2 \log n) for each iteration, where n is the number of variables and k is a bound on the treewidth. We compare our approach to state-of-the-art methods on synthetic datasets and classical benchmarks, showing the gains of the novel convex approach. ER -
APA
Kumar, K.S.S. & Bach, F.. (2013). Convex Relaxations for Learning Bounded-Treewidth Decomposable Graphs. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(1):525-533 Available from https://proceedings.mlr.press/v28/kumar13c.html.

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