On Time Varying Undirected Graphs

Mladen Kolar, Eric P. Xing
Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, PMLR 15:407-415, 2011.

Abstract

The time-varying multivariate Gaussian distribution and the undirected graph associated with it, as introduced in Zhou et al. (2008), provide a useful statistical framework for modeling complex dynamic networks. In many application domains, it is of high importance to estimate the graph structure of the model consistently for the purpose of scientific discovery. In this short note, we show that under suitable technical conditions the structure of the undirected graphical model can be consistently estimated in the high dimensional setting, when the dimensionality of the model is allowed to diverge with the sample size. The model selection consistency is shown for the procedure proposed in Zhou et al. (2008) and for the modified neighborhood selection procedure of Meinshausen and Bühlmann (2006).

Cite this Paper

BibTeX
@InProceedings{pmlr-v15-kolar11a, title = {On Time Varying Undirected Graphs}, author = {Kolar, Mladen and Xing, Eric P.}, booktitle = {Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics}, pages = {407--415}, year = {2011}, editor = {Gordon, Geoffrey and Dunson, David and Dudík, Miroslav}, volume = {15}, series = {Proceedings of Machine Learning Research}, address = {Fort Lauderdale, FL, USA}, month = {11--13 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v15/kolar11a/kolar11a.pdf}, url = {https://proceedings.mlr.press/v15/kolar11a.html}, abstract = {The time-varying multivariate Gaussian distribution and the undirected graph associated with it, as introduced in Zhou et al. (2008), provide a useful statistical framework for modeling complex dynamic networks. In many application domains, it is of high importance to estimate the graph structure of the model consistently for the purpose of scientific discovery. In this short note, we show that under suitable technical conditions the structure of the undirected graphical model can be consistently estimated in the high dimensional setting, when the dimensionality of the model is allowed to diverge with the sample size. The model selection consistency is shown for the procedure proposed in Zhou et al. (2008) and for the modified neighborhood selection procedure of Meinshausen and Bühlmann (2006).} }
Endnote
%0 Conference Paper %T On Time Varying Undirected Graphs %A Mladen Kolar %A Eric P. Xing %B Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2011 %E Geoffrey Gordon %E David Dunson %E Miroslav Dudík %F pmlr-v15-kolar11a %I PMLR %P 407--415 %U https://proceedings.mlr.press/v15/kolar11a.html %V 15 %X The time-varying multivariate Gaussian distribution and the undirected graph associated with it, as introduced in Zhou et al. (2008), provide a useful statistical framework for modeling complex dynamic networks. In many application domains, it is of high importance to estimate the graph structure of the model consistently for the purpose of scientific discovery. In this short note, we show that under suitable technical conditions the structure of the undirected graphical model can be consistently estimated in the high dimensional setting, when the dimensionality of the model is allowed to diverge with the sample size. The model selection consistency is shown for the procedure proposed in Zhou et al. (2008) and for the modified neighborhood selection procedure of Meinshausen and Bühlmann (2006).
RIS
TY - CPAPER TI - On Time Varying Undirected Graphs AU - Mladen Kolar AU - Eric P. Xing BT - Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics DA - 2011/06/14 ED - Geoffrey Gordon ED - David Dunson ED - Miroslav Dudík ID - pmlr-v15-kolar11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 15 SP - 407 EP - 415 L1 - http://proceedings.mlr.press/v15/kolar11a/kolar11a.pdf UR - https://proceedings.mlr.press/v15/kolar11a.html AB - The time-varying multivariate Gaussian distribution and the undirected graph associated with it, as introduced in Zhou et al. (2008), provide a useful statistical framework for modeling complex dynamic networks. In many application domains, it is of high importance to estimate the graph structure of the model consistently for the purpose of scientific discovery. In this short note, we show that under suitable technical conditions the structure of the undirected graphical model can be consistently estimated in the high dimensional setting, when the dimensionality of the model is allowed to diverge with the sample size. The model selection consistency is shown for the procedure proposed in Zhou et al. (2008) and for the modified neighborhood selection procedure of Meinshausen and Bühlmann (2006). ER -
APA
Kolar, M. & Xing, E.P.. (2011). On Time Varying Undirected Graphs. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 15:407-415 Available from https://proceedings.mlr.press/v15/kolar11a.html.

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