Learning Markov Networks With Arithmetic Circuits

Daniel Lowd, Amirmohammad Rooshenas
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:406-414, 2013.

Abstract

Markov networks are an effective way to represent complex probability distributions. However, learning their structure and parameters or using them to answer queries is typically intractable. One approach to making learning and inference tractable is to use approximations, such as pseudo-likelihood or approximate inference. An alternate approach is to use a restricted class of models where exact inference is always efficient. Previous work has explored low treewidth models, models with tree-structured features, and latent variable models. In this paper, we introduce ACMN, the first ever method for learning efficient Markov networks with arbitrary conjunctive features. The secret to ACMN’s greater flexibility is its use of arithmetic circuits, a linear-time inference representation that can handle many high treewidth models by exploiting local structure. ACMN uses the size of the corresponding arithmetic circuit as a learning bias, allowing it to trade off accuracy and inference complexity. In experiments on 12 standard datasets, the tractable models learned by ACMN are more accurate than both tractable models learned by other algorithms and approximate inference in intractable models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v31-lowd13a, title = {Learning Markov Networks With Arithmetic Circuits}, author = {Lowd, Daniel and Rooshenas, Amirmohammad}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {406--414}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/lowd13a.pdf}, url = {https://proceedings.mlr.press/v31/lowd13a.html}, abstract = {Markov networks are an effective way to represent complex probability distributions. However, learning their structure and parameters or using them to answer queries is typically intractable. One approach to making learning and inference tractable is to use approximations, such as pseudo-likelihood or approximate inference. An alternate approach is to use a restricted class of models where exact inference is always efficient. Previous work has explored low treewidth models, models with tree-structured features, and latent variable models. In this paper, we introduce ACMN, the first ever method for learning efficient Markov networks with arbitrary conjunctive features. The secret to ACMN’s greater flexibility is its use of arithmetic circuits, a linear-time inference representation that can handle many high treewidth models by exploiting local structure. ACMN uses the size of the corresponding arithmetic circuit as a learning bias, allowing it to trade off accuracy and inference complexity. In experiments on 12 standard datasets, the tractable models learned by ACMN are more accurate than both tractable models learned by other algorithms and approximate inference in intractable models. } }
Endnote
%0 Conference Paper %T Learning Markov Networks With Arithmetic Circuits %A Daniel Lowd %A Amirmohammad Rooshenas %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-lowd13a %I PMLR %P 406--414 %U https://proceedings.mlr.press/v31/lowd13a.html %V 31 %X Markov networks are an effective way to represent complex probability distributions. However, learning their structure and parameters or using them to answer queries is typically intractable. One approach to making learning and inference tractable is to use approximations, such as pseudo-likelihood or approximate inference. An alternate approach is to use a restricted class of models where exact inference is always efficient. Previous work has explored low treewidth models, models with tree-structured features, and latent variable models. In this paper, we introduce ACMN, the first ever method for learning efficient Markov networks with arbitrary conjunctive features. The secret to ACMN’s greater flexibility is its use of arithmetic circuits, a linear-time inference representation that can handle many high treewidth models by exploiting local structure. ACMN uses the size of the corresponding arithmetic circuit as a learning bias, allowing it to trade off accuracy and inference complexity. In experiments on 12 standard datasets, the tractable models learned by ACMN are more accurate than both tractable models learned by other algorithms and approximate inference in intractable models.
RIS
TY - CPAPER TI - Learning Markov Networks With Arithmetic Circuits AU - Daniel Lowd AU - Amirmohammad Rooshenas BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-lowd13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 406 EP - 414 L1 - http://proceedings.mlr.press/v31/lowd13a.pdf UR - https://proceedings.mlr.press/v31/lowd13a.html AB - Markov networks are an effective way to represent complex probability distributions. However, learning their structure and parameters or using them to answer queries is typically intractable. One approach to making learning and inference tractable is to use approximations, such as pseudo-likelihood or approximate inference. An alternate approach is to use a restricted class of models where exact inference is always efficient. Previous work has explored low treewidth models, models with tree-structured features, and latent variable models. In this paper, we introduce ACMN, the first ever method for learning efficient Markov networks with arbitrary conjunctive features. The secret to ACMN’s greater flexibility is its use of arithmetic circuits, a linear-time inference representation that can handle many high treewidth models by exploiting local structure. ACMN uses the size of the corresponding arithmetic circuit as a learning bias, allowing it to trade off accuracy and inference complexity. In experiments on 12 standard datasets, the tractable models learned by ACMN are more accurate than both tractable models learned by other algorithms and approximate inference in intractable models. ER -
APA
Lowd, D. & Rooshenas, A.. (2013). Learning Markov Networks With Arithmetic Circuits. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:406-414 Available from https://proceedings.mlr.press/v31/lowd13a.html.

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