High-dimensional Mixed Graphical Model with Ordinal Data: Parameter Estimation and Statistical Inference

Huijie Feng, Yang Ning
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:654-663, 2019.

Abstract

We consider parameter estimation and statistical inference of high-dimensional undirected graphical models for mixed data comprising both ordinal and continuous variables. We propose a flexible model called Latent Mixed Gaussian Copula Model that simultaneously deals with such mixed data by assuming that the observed ordinal variables are generated by latent variables. For parameter estimation, we introduce a convenient rank-based ensemble approach to estimate the latent correlation matrix, which can be subsequently applied to recover the latent graph structure. In addition, based on the ensemble estimator, we develop test statistics via a pseudo-likelihood approach to quantify the uncertainty associated with the low dimensional components of high-dimensional parameters. Our theoretical analysis shows the consistency of the estimator and asymptotic normality of the test statistic. Experiments on simulated and real gene expression data are conducted to validate our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-feng19a, title = {High-dimensional Mixed Graphical Model with Ordinal Data: Parameter Estimation and Statistical Inference}, author = {Feng, Huijie and Ning, Yang}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {654--663}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/feng19a/feng19a.pdf}, url = {https://proceedings.mlr.press/v89/feng19a.html}, abstract = {We consider parameter estimation and statistical inference of high-dimensional undirected graphical models for mixed data comprising both ordinal and continuous variables. We propose a flexible model called Latent Mixed Gaussian Copula Model that simultaneously deals with such mixed data by assuming that the observed ordinal variables are generated by latent variables. For parameter estimation, we introduce a convenient rank-based ensemble approach to estimate the latent correlation matrix, which can be subsequently applied to recover the latent graph structure. In addition, based on the ensemble estimator, we develop test statistics via a pseudo-likelihood approach to quantify the uncertainty associated with the low dimensional components of high-dimensional parameters. Our theoretical analysis shows the consistency of the estimator and asymptotic normality of the test statistic. Experiments on simulated and real gene expression data are conducted to validate our approach.} }
Endnote
%0 Conference Paper %T High-dimensional Mixed Graphical Model with Ordinal Data: Parameter Estimation and Statistical Inference %A Huijie Feng %A Yang Ning %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-feng19a %I PMLR %P 654--663 %U https://proceedings.mlr.press/v89/feng19a.html %V 89 %X We consider parameter estimation and statistical inference of high-dimensional undirected graphical models for mixed data comprising both ordinal and continuous variables. We propose a flexible model called Latent Mixed Gaussian Copula Model that simultaneously deals with such mixed data by assuming that the observed ordinal variables are generated by latent variables. For parameter estimation, we introduce a convenient rank-based ensemble approach to estimate the latent correlation matrix, which can be subsequently applied to recover the latent graph structure. In addition, based on the ensemble estimator, we develop test statistics via a pseudo-likelihood approach to quantify the uncertainty associated with the low dimensional components of high-dimensional parameters. Our theoretical analysis shows the consistency of the estimator and asymptotic normality of the test statistic. Experiments on simulated and real gene expression data are conducted to validate our approach.
APA
Feng, H. & Ning, Y.. (2019). High-dimensional Mixed Graphical Model with Ordinal Data: Parameter Estimation and Statistical Inference. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:654-663 Available from https://proceedings.mlr.press/v89/feng19a.html.

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