Learning High-dimensional Gaussian Graphical Models under Total Positivity without Adjustment of Tuning Parameters

Yuhao Wang, Uma Roy, Caroline Uhler
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2698-2708, 2020.

Abstract

We consider the problem of estimating an undirected Gaussian graphical model when the underlying distribution is multivariate totally positive of order 2 (MTP2), a strong form of positive dependence. Such distributions are relevant for example for portfolio selection, since assets are usually positively dependent. A large body of methods have been proposed for learning undirected graphical models without the MTP2 constraint. A major limitation of these methods is that their structure recovery guarantees in the high-dimensional setting usually require a particular choice of a tuning parameter, which is unknown a priori in real world applications. We here propose a new method to estimate the underlying undirected graphical model under MTP2 and show that it is provably consistent in structure recovery without adjusting the tuning parameters. This is achieved by a constraint-based estimator that infers the structure of the underlying graphical model by testing the signs of the empirical partial correlation coefficients. We evaluate the performance of our estimator in simulations and on financial data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-wang20g, title = {Learning High-dimensional Gaussian Graphical Models under Total Positivity without Adjustment of Tuning Parameters}, author = {Wang, Yuhao and Roy, Uma and Uhler, Caroline}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2698--2708}, 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/wang20g/wang20g.pdf}, url = {https://proceedings.mlr.press/v108/wang20g.html}, abstract = {We consider the problem of estimating an undirected Gaussian graphical model when the underlying distribution is multivariate totally positive of order 2 (MTP2), a strong form of positive dependence. Such distributions are relevant for example for portfolio selection, since assets are usually positively dependent. A large body of methods have been proposed for learning undirected graphical models without the MTP2 constraint. A major limitation of these methods is that their structure recovery guarantees in the high-dimensional setting usually require a particular choice of a tuning parameter, which is unknown a priori in real world applications. We here propose a new method to estimate the underlying undirected graphical model under MTP2 and show that it is provably consistent in structure recovery without adjusting the tuning parameters. This is achieved by a constraint-based estimator that infers the structure of the underlying graphical model by testing the signs of the empirical partial correlation coefficients. We evaluate the performance of our estimator in simulations and on financial data.} }
Endnote
%0 Conference Paper %T Learning High-dimensional Gaussian Graphical Models under Total Positivity without Adjustment of Tuning Parameters %A Yuhao Wang %A Uma Roy %A Caroline Uhler %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-wang20g %I PMLR %P 2698--2708 %U https://proceedings.mlr.press/v108/wang20g.html %V 108 %X We consider the problem of estimating an undirected Gaussian graphical model when the underlying distribution is multivariate totally positive of order 2 (MTP2), a strong form of positive dependence. Such distributions are relevant for example for portfolio selection, since assets are usually positively dependent. A large body of methods have been proposed for learning undirected graphical models without the MTP2 constraint. A major limitation of these methods is that their structure recovery guarantees in the high-dimensional setting usually require a particular choice of a tuning parameter, which is unknown a priori in real world applications. We here propose a new method to estimate the underlying undirected graphical model under MTP2 and show that it is provably consistent in structure recovery without adjusting the tuning parameters. This is achieved by a constraint-based estimator that infers the structure of the underlying graphical model by testing the signs of the empirical partial correlation coefficients. We evaluate the performance of our estimator in simulations and on financial data.
APA
Wang, Y., Roy, U. & Uhler, C.. (2020). Learning High-dimensional Gaussian Graphical Models under Total Positivity without Adjustment of Tuning Parameters. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2698-2708 Available from https://proceedings.mlr.press/v108/wang20g.html.

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