Graphical Model Selection for Gaussian Conditional Random Fields in the Presence of Latent Variables
成果类型：
Article
署名作者：
Frot, Benjamin; Jostins, Luke; McVean, Gilean
署名单位：
University of Oxford; University of Oxford; Wellcome Centre for Human Genetics; University of Oxford; Kennedy Institute for Rheumatology; University of Oxford
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2018.1434531
发表日期：
2019
页码：
723-734
关键词：
摘要：
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random field into the sum of a sparse and a low-rank matrix. We derive convergence bounds for this estimator and show that it is well-behaved in the high-dimensional regime as well as sparsistent (i.e., capable of recovering the graph structure). We then show how proximal gradient algorithms and semi-definite programming techniques can be employed to fit the model to thousands of variables. Through extensive simulations, we illustrate the conditions required for identifiability and show that there is a wide range of situations in which this model performs significantly better than its counterparts, for example, by accommodating more latent variables. Finally, the suggested method is applied to two datasets comprising individual level data on genetic variants and metabolites levels. We show our results replicate better than alternative approaches and show enriched biological signal. Supplementary materials for this article are available online.
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