Variable Selection for Gaussian Graphical Models

Jean Honorio, Dimitris Samaras, Irina Rish, Guillermo Cecchi
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:538-546, 2012.

Abstract

We present a variable-selection structure learning approach for Gaussian graphical models. Unlike standard sparseness promoting techniques, our method aims at selecting the most-important variables besides simply sparsifying the set of edges. Through simulations, we show that our method outperforms the state-of-the-art in recovering the ground truth model. Our method also exhibits better generalization performance in a wide range of complex real-world datasets: brain fMRI, gene expression, NASDAQ stock prices and world weather. We also show that our resulting networks are more interpretable in the context of brain fMRI analysis, while retaining discriminability. From an optimization perspective, we show that a block coordinate descent method generates a sequence of positive definite solutions. Thus, we reduce the original problem into a sequence of strictly convex (\ell_1,\ell_p) regularized quadratic minimization subproblems for p∈{2,∞}. Our algorithm is well founded since the optimal solution of the maximization problem is unique and bounded.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-honorio12, title = {Variable Selection for Gaussian Graphical Models}, author = {Honorio, Jean and Samaras, Dimitris and Rish, Irina and Cecchi, Guillermo}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {538--546}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/honorio12/honorio12.pdf}, url = {https://proceedings.mlr.press/v22/honorio12.html}, abstract = {We present a variable-selection structure learning approach for Gaussian graphical models. Unlike standard sparseness promoting techniques, our method aims at selecting the most-important variables besides simply sparsifying the set of edges. Through simulations, we show that our method outperforms the state-of-the-art in recovering the ground truth model. Our method also exhibits better generalization performance in a wide range of complex real-world datasets: brain fMRI, gene expression, NASDAQ stock prices and world weather. We also show that our resulting networks are more interpretable in the context of brain fMRI analysis, while retaining discriminability. From an optimization perspective, we show that a block coordinate descent method generates a sequence of positive definite solutions. Thus, we reduce the original problem into a sequence of strictly convex (\ell_1,\ell_p) regularized quadratic minimization subproblems for p∈{2,∞}. Our algorithm is well founded since the optimal solution of the maximization problem is unique and bounded.} }
Endnote
%0 Conference Paper %T Variable Selection for Gaussian Graphical Models %A Jean Honorio %A Dimitris Samaras %A Irina Rish %A Guillermo Cecchi %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-honorio12 %I PMLR %P 538--546 %U https://proceedings.mlr.press/v22/honorio12.html %V 22 %X We present a variable-selection structure learning approach for Gaussian graphical models. Unlike standard sparseness promoting techniques, our method aims at selecting the most-important variables besides simply sparsifying the set of edges. Through simulations, we show that our method outperforms the state-of-the-art in recovering the ground truth model. Our method also exhibits better generalization performance in a wide range of complex real-world datasets: brain fMRI, gene expression, NASDAQ stock prices and world weather. We also show that our resulting networks are more interpretable in the context of brain fMRI analysis, while retaining discriminability. From an optimization perspective, we show that a block coordinate descent method generates a sequence of positive definite solutions. Thus, we reduce the original problem into a sequence of strictly convex (\ell_1,\ell_p) regularized quadratic minimization subproblems for p∈{2,∞}. Our algorithm is well founded since the optimal solution of the maximization problem is unique and bounded.
RIS
TY - CPAPER TI - Variable Selection for Gaussian Graphical Models AU - Jean Honorio AU - Dimitris Samaras AU - Irina Rish AU - Guillermo Cecchi BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-honorio12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 538 EP - 546 L1 - http://proceedings.mlr.press/v22/honorio12/honorio12.pdf UR - https://proceedings.mlr.press/v22/honorio12.html AB - We present a variable-selection structure learning approach for Gaussian graphical models. Unlike standard sparseness promoting techniques, our method aims at selecting the most-important variables besides simply sparsifying the set of edges. Through simulations, we show that our method outperforms the state-of-the-art in recovering the ground truth model. Our method also exhibits better generalization performance in a wide range of complex real-world datasets: brain fMRI, gene expression, NASDAQ stock prices and world weather. We also show that our resulting networks are more interpretable in the context of brain fMRI analysis, while retaining discriminability. From an optimization perspective, we show that a block coordinate descent method generates a sequence of positive definite solutions. Thus, we reduce the original problem into a sequence of strictly convex (\ell_1,\ell_p) regularized quadratic minimization subproblems for p∈{2,∞}. Our algorithm is well founded since the optimal solution of the maximization problem is unique and bounded. ER -
APA
Honorio, J., Samaras, D., Rish, I. & Cecchi, G.. (2012). Variable Selection for Gaussian Graphical Models. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:538-546 Available from https://proceedings.mlr.press/v22/honorio12.html.

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