Constrained approximate maximum entropy learning of Markov random fields

Varun Ganapathi, David Vickrey, John Duchi, Daphne Koller
Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence, PMLR R6:196-203, 2008.

Abstract

Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a different approach for combining MRF learning and Bethe approximation. We consider the dual of maximum likelihood Markov network learning — maximizing entropy with moment matching constraints — and then approximate both the objective and the constraints in the resulting optimization problem. Unlike previous work along these lines (Teh & Welling, 2003), our formulation allows parameter sharing between features in a general log-linear model, parameter regularization and conditional training. We show that piecewise training (Sutton & McCallum, 2005) is a very restricted special case of this formulation. We study two optimization strategies: one based on a single convex approximation and one that uses repeated convex approximations. We show results on several real-world networks that demonstrate that these algorithms can significantly outperform learning with loopy and piece-wise. Our results also provide a framework for analyzing the trade-offs of different relaxations of the entropy objective and of the constraints.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR6-ganapathi08a, title = {Constrained approximate maximum entropy learning of Markov random fields}, author = {Ganapathi, Varun and Vickrey, David and Duchi, John and Koller, Daphne}, booktitle = {Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence}, pages = {196--203}, year = {2008}, editor = {McAllester, David A. and Myllymäki, Petri}, volume = {R6}, series = {Proceedings of Machine Learning Research}, month = {09--12 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r6/main/assets/ganapathi08a/ganapathi08a.pdf}, url = {https://proceedings.mlr.press/r6/ganapathi08a.html}, abstract = {Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a different approach for combining MRF learning and Bethe approximation. We consider the dual of maximum likelihood Markov network learning — maximizing entropy with moment matching constraints — and then approximate both the objective and the constraints in the resulting optimization problem. Unlike previous work along these lines (Teh & Welling, 2003), our formulation allows parameter sharing between features in a general log-linear model, parameter regularization and conditional training. We show that piecewise training (Sutton & McCallum, 2005) is a very restricted special case of this formulation. We study two optimization strategies: one based on a single convex approximation and one that uses repeated convex approximations. We show results on several real-world networks that demonstrate that these algorithms can significantly outperform learning with loopy and piece-wise. Our results also provide a framework for analyzing the trade-offs of different relaxations of the entropy objective and of the constraints.}, note = {Reissued by PMLR on 09 October 2024.} }
Endnote
%0 Conference Paper %T Constrained approximate maximum entropy learning of Markov random fields %A Varun Ganapathi %A David Vickrey %A John Duchi %A Daphne Koller %B Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2008 %E David A. McAllester %E Petri Myllymäki %F pmlr-vR6-ganapathi08a %I PMLR %P 196--203 %U https://proceedings.mlr.press/r6/ganapathi08a.html %V R6 %X Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a different approach for combining MRF learning and Bethe approximation. We consider the dual of maximum likelihood Markov network learning — maximizing entropy with moment matching constraints — and then approximate both the objective and the constraints in the resulting optimization problem. Unlike previous work along these lines (Teh & Welling, 2003), our formulation allows parameter sharing between features in a general log-linear model, parameter regularization and conditional training. We show that piecewise training (Sutton & McCallum, 2005) is a very restricted special case of this formulation. We study two optimization strategies: one based on a single convex approximation and one that uses repeated convex approximations. We show results on several real-world networks that demonstrate that these algorithms can significantly outperform learning with loopy and piece-wise. Our results also provide a framework for analyzing the trade-offs of different relaxations of the entropy objective and of the constraints. %Z Reissued by PMLR on 09 October 2024.
APA
Ganapathi, V., Vickrey, D., Duchi, J. & Koller, D.. (2008). Constrained approximate maximum entropy learning of Markov random fields. Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R6:196-203 Available from https://proceedings.mlr.press/r6/ganapathi08a.html. Reissued by PMLR on 09 October 2024.

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