The Bigraphical Lasso

Alfredo Kalaitzis, John Lafferty, Neil D. Lawrence, Shuheng Zhou
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1229-1237, 2013.

Abstract

The i.i.d. assumption in machine learning is endemic, but often flawed. Complex data sets exhibit partial correlations between both instances and features. A model specifying both types of correlation can have a number of parameters that scales quadratically with the number of features and data points. We introduce the bigraphical lasso, an estimator for precision matrices of matrix-normals based on the Cartesian product of graphs. A prominent product in spectral graph theory, this structure has appealing properties for regression, enhanced sparsity and interpretability. To deal with the parameter explosion we introduce L1 penalties and fit the model through a flip-flop algorithm that results in a linear number of lasso regressions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-kalaitzis13, title = {The Bigraphical Lasso}, author = {Kalaitzis, Alfredo and Lafferty, John and Lawrence, Neil D. and Zhou, Shuheng}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {1229--1237}, 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/kalaitzis13.pdf}, url = {https://proceedings.mlr.press/v28/kalaitzis13.html}, abstract = {The i.i.d. assumption in machine learning is endemic, but often flawed. Complex data sets exhibit partial correlations between both instances and features. A model specifying both types of correlation can have a number of parameters that scales quadratically with the number of features and data points. We introduce the bigraphical lasso, an estimator for precision matrices of matrix-normals based on the Cartesian product of graphs. A prominent product in spectral graph theory, this structure has appealing properties for regression, enhanced sparsity and interpretability. To deal with the parameter explosion we introduce L1 penalties and fit the model through a flip-flop algorithm that results in a linear number of lasso regressions.} }
Endnote
%0 Conference Paper %T The Bigraphical Lasso %A Alfredo Kalaitzis %A John Lafferty %A Neil D. Lawrence %A Shuheng Zhou %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-kalaitzis13 %I PMLR %P 1229--1237 %U https://proceedings.mlr.press/v28/kalaitzis13.html %V 28 %N 3 %X The i.i.d. assumption in machine learning is endemic, but often flawed. Complex data sets exhibit partial correlations between both instances and features. A model specifying both types of correlation can have a number of parameters that scales quadratically with the number of features and data points. We introduce the bigraphical lasso, an estimator for precision matrices of matrix-normals based on the Cartesian product of graphs. A prominent product in spectral graph theory, this structure has appealing properties for regression, enhanced sparsity and interpretability. To deal with the parameter explosion we introduce L1 penalties and fit the model through a flip-flop algorithm that results in a linear number of lasso regressions.
RIS
TY - CPAPER TI - The Bigraphical Lasso AU - Alfredo Kalaitzis AU - John Lafferty AU - Neil D. Lawrence AU - Shuheng Zhou BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/26 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-kalaitzis13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 3 SP - 1229 EP - 1237 L1 - http://proceedings.mlr.press/v28/kalaitzis13.pdf UR - https://proceedings.mlr.press/v28/kalaitzis13.html AB - The i.i.d. assumption in machine learning is endemic, but often flawed. Complex data sets exhibit partial correlations between both instances and features. A model specifying both types of correlation can have a number of parameters that scales quadratically with the number of features and data points. We introduce the bigraphical lasso, an estimator for precision matrices of matrix-normals based on the Cartesian product of graphs. A prominent product in spectral graph theory, this structure has appealing properties for regression, enhanced sparsity and interpretability. To deal with the parameter explosion we introduce L1 penalties and fit the model through a flip-flop algorithm that results in a linear number of lasso regressions. ER -
APA
Kalaitzis, A., Lafferty, J., Lawrence, N.D. & Zhou, S.. (2013). The Bigraphical Lasso. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(3):1229-1237 Available from https://proceedings.mlr.press/v28/kalaitzis13.html.

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