Markov Network Estimation From Multi-attribute Data

Mladen Kolar, Han Liu, Eric Xing
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):73-81, 2013.

Abstract

Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such data, neither can the theories developed around such methods be directly applied. In this paper, we propose a new principled framework for estimating multi-attribute graphs. Instead of estimating the partial correlation as in current literature, our method estimates the partial canonical correlations that naturally accommodate complex nodal features. Computationally, we provide an efficient algorithm which utilizes the multi-attribute structure. Theoretically, we provide sufficient conditions which guarantee consistent graph recovery. Extensive simulation studies demonstrate performance of our method under various conditions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-kolar13a, title = {Markov Network Estimation From Multi-attribute Data}, author = {Kolar, Mladen and Liu, Han and Xing, Eric}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {73--81}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/kolar13a.pdf}, url = {https://proceedings.mlr.press/v28/kolar13a.html}, abstract = {Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such data, neither can the theories developed around such methods be directly applied. In this paper, we propose a new principled framework for estimating multi-attribute graphs. Instead of estimating the partial correlation as in current literature, our method estimates the partial canonical correlations that naturally accommodate complex nodal features. Computationally, we provide an efficient algorithm which utilizes the multi-attribute structure. Theoretically, we provide sufficient conditions which guarantee consistent graph recovery. Extensive simulation studies demonstrate performance of our method under various conditions.} }
Endnote
%0 Conference Paper %T Markov Network Estimation From Multi-attribute Data %A Mladen Kolar %A Han Liu %A Eric Xing %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-kolar13a %I PMLR %P 73--81 %U https://proceedings.mlr.press/v28/kolar13a.html %V 28 %N 3 %X Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such data, neither can the theories developed around such methods be directly applied. In this paper, we propose a new principled framework for estimating multi-attribute graphs. Instead of estimating the partial correlation as in current literature, our method estimates the partial canonical correlations that naturally accommodate complex nodal features. Computationally, we provide an efficient algorithm which utilizes the multi-attribute structure. Theoretically, we provide sufficient conditions which guarantee consistent graph recovery. Extensive simulation studies demonstrate performance of our method under various conditions.
RIS
TY - CPAPER TI - Markov Network Estimation From Multi-attribute Data AU - Mladen Kolar AU - Han Liu AU - Eric Xing BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/26 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-kolar13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 3 SP - 73 EP - 81 L1 - http://proceedings.mlr.press/v28/kolar13a.pdf UR - https://proceedings.mlr.press/v28/kolar13a.html AB - Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such data, neither can the theories developed around such methods be directly applied. In this paper, we propose a new principled framework for estimating multi-attribute graphs. Instead of estimating the partial correlation as in current literature, our method estimates the partial canonical correlations that naturally accommodate complex nodal features. Computationally, we provide an efficient algorithm which utilizes the multi-attribute structure. Theoretically, we provide sufficient conditions which guarantee consistent graph recovery. Extensive simulation studies demonstrate performance of our method under various conditions. ER -
APA
Kolar, M., Liu, H. & Xing, E.. (2013). Markov Network Estimation From Multi-attribute Data. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(3):73-81 Available from https://proceedings.mlr.press/v28/kolar13a.html.

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