Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials

Mark Schmidt, Kevin Murphy
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:709-716, 2010.

Abstract

Previous work has examined structure learning in log-linear models with $\ell_1$-regularization, largely focusing on the case of pairwise potentials. In this work we consider the case of models with potentials of arbitrary order, but that satisfy a hierarchical constraint. We enforce the hierarchical constraint using group $\ell_1$-regularization with overlapping groups, and an active set method that enforces hierarchical inclusion allows us to tractably consider the exponential number of higher-order potentials. We use a spectral projected gradient method as a sub-routine for solving the overlapping group $\ell_1$-regularization problem, and make use of a sparse version of Dykstra’s algorithm to compute the projection. Our experiments indicate that this model gives equal or better test set likelihood compared to previous models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-schmidt10a, title = {Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials}, author = {Schmidt, Mark and Murphy, Kevin}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {709--716}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/schmidt10a/schmidt10a.pdf}, url = {https://proceedings.mlr.press/v9/schmidt10a.html}, abstract = {Previous work has examined structure learning in log-linear models with $\ell_1$-regularization, largely focusing on the case of pairwise potentials. In this work we consider the case of models with potentials of arbitrary order, but that satisfy a hierarchical constraint. We enforce the hierarchical constraint using group $\ell_1$-regularization with overlapping groups, and an active set method that enforces hierarchical inclusion allows us to tractably consider the exponential number of higher-order potentials. We use a spectral projected gradient method as a sub-routine for solving the overlapping group $\ell_1$-regularization problem, and make use of a sparse version of Dykstra’s algorithm to compute the projection. Our experiments indicate that this model gives equal or better test set likelihood compared to previous models.} }
Endnote
%0 Conference Paper %T Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials %A Mark Schmidt %A Kevin Murphy %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-schmidt10a %I PMLR %P 709--716 %U https://proceedings.mlr.press/v9/schmidt10a.html %V 9 %X Previous work has examined structure learning in log-linear models with $\ell_1$-regularization, largely focusing on the case of pairwise potentials. In this work we consider the case of models with potentials of arbitrary order, but that satisfy a hierarchical constraint. We enforce the hierarchical constraint using group $\ell_1$-regularization with overlapping groups, and an active set method that enforces hierarchical inclusion allows us to tractably consider the exponential number of higher-order potentials. We use a spectral projected gradient method as a sub-routine for solving the overlapping group $\ell_1$-regularization problem, and make use of a sparse version of Dykstra’s algorithm to compute the projection. Our experiments indicate that this model gives equal or better test set likelihood compared to previous models.
RIS
TY - CPAPER TI - Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials AU - Mark Schmidt AU - Kevin Murphy BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-schmidt10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 709 EP - 716 L1 - http://proceedings.mlr.press/v9/schmidt10a/schmidt10a.pdf UR - https://proceedings.mlr.press/v9/schmidt10a.html AB - Previous work has examined structure learning in log-linear models with $\ell_1$-regularization, largely focusing on the case of pairwise potentials. In this work we consider the case of models with potentials of arbitrary order, but that satisfy a hierarchical constraint. We enforce the hierarchical constraint using group $\ell_1$-regularization with overlapping groups, and an active set method that enforces hierarchical inclusion allows us to tractably consider the exponential number of higher-order potentials. We use a spectral projected gradient method as a sub-routine for solving the overlapping group $\ell_1$-regularization problem, and make use of a sparse version of Dykstra’s algorithm to compute the projection. Our experiments indicate that this model gives equal or better test set likelihood compared to previous models. ER -
APA
Schmidt, M. & Murphy, K.. (2010). Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:709-716 Available from https://proceedings.mlr.press/v9/schmidt10a.html.

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