Multi-level Gaussian Graphical Models Conditional on Covariates

Gi Bum Kim, Seyoung Kim
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:4216-4225, 2020.

Abstract

We address the problem of learning the structure of a high-dimensional Gaussian graphical model conditional on covariates, when each sample belongs to groups at multiple levels of hierarchy. The existing statistical methods for learning covariate-conditioned Gaussian graphical models focused on learning the aggregate behavior of inputs and outputs in a single-layer network. We propose a statistical model called multi-level conditional Gaussian graphical models for modeling multi-level output networks influenced by both individual-level and group-level inputs. We describe a decomposition of our model into a product of two components, one for sum variables and the other for difference variables derived from the original variables. This decomposition leads to an efficient learning algorithm for both complete data and incomplete data with randomly missing individual observations, as the expensive repeated computation of the partition function can be avoided. We demonstrate our method on simulated data and real-world data in finance and genomics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-kim20d, title = {Multi-level Gaussian Graphical Models Conditional on Covariates}, author = {Kim, Gi Bum and Kim, Seyoung}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {4216--4225}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/kim20d/kim20d.pdf}, url = {https://proceedings.mlr.press/v108/kim20d.html}, abstract = {We address the problem of learning the structure of a high-dimensional Gaussian graphical model conditional on covariates, when each sample belongs to groups at multiple levels of hierarchy. The existing statistical methods for learning covariate-conditioned Gaussian graphical models focused on learning the aggregate behavior of inputs and outputs in a single-layer network. We propose a statistical model called multi-level conditional Gaussian graphical models for modeling multi-level output networks influenced by both individual-level and group-level inputs. We describe a decomposition of our model into a product of two components, one for sum variables and the other for difference variables derived from the original variables. This decomposition leads to an efficient learning algorithm for both complete data and incomplete data with randomly missing individual observations, as the expensive repeated computation of the partition function can be avoided. We demonstrate our method on simulated data and real-world data in finance and genomics.} }
Endnote
%0 Conference Paper %T Multi-level Gaussian Graphical Models Conditional on Covariates %A Gi Bum Kim %A Seyoung Kim %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-kim20d %I PMLR %P 4216--4225 %U https://proceedings.mlr.press/v108/kim20d.html %V 108 %X We address the problem of learning the structure of a high-dimensional Gaussian graphical model conditional on covariates, when each sample belongs to groups at multiple levels of hierarchy. The existing statistical methods for learning covariate-conditioned Gaussian graphical models focused on learning the aggregate behavior of inputs and outputs in a single-layer network. We propose a statistical model called multi-level conditional Gaussian graphical models for modeling multi-level output networks influenced by both individual-level and group-level inputs. We describe a decomposition of our model into a product of two components, one for sum variables and the other for difference variables derived from the original variables. This decomposition leads to an efficient learning algorithm for both complete data and incomplete data with randomly missing individual observations, as the expensive repeated computation of the partition function can be avoided. We demonstrate our method on simulated data and real-world data in finance and genomics.
APA
Kim, G.B. & Kim, S.. (2020). Multi-level Gaussian Graphical Models Conditional on Covariates. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:4216-4225 Available from https://proceedings.mlr.press/v108/kim20d.html.

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