Graphical Model Selection for Gaussian Conditional Random Fields in the Presence of Latent Variables

Journal of the American Statistical Association
Benjamin FrotGilean McVean

Abstract

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.

References

Dec 15, 2007·Biostatistics·Jerome FriedmanRobert Tibshirani
Nov 11, 2010·Genetics·Frank W Stearns
May 6, 2011·Nucleic Acids Research·Jiguang WangXiang-Sun Zhang
Apr 18, 2012·International Journal of Epidemiology·Abigail FraserDebbie A Lawlor
Apr 18, 2012·International Journal of Epidemiology·Andy BoydGeorge Davey Smith
Aug 21, 2012·The Annals of Applied Statistics·Jianxin Yin, Hongzhe Li
Nov 28, 2012·Nucleic Acids Research·Janna HastingsChristoph Steinbeck
Mar 4, 2014·PLoS Computational Biology·Lingxue Zhang, Seyoung Kim

❮ Previous
Next ❯

Citations

Oct 24, 2020·PLoS Computational Biology·Calvin McCarterSeyoung Kim

❮ Previous
Next ❯

Software Mentioned

Logdet
LSCGGM
SDPT3
LogdetPPA
MATLAB
SCGGM
GLASSO
PPA

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

IEEE Transactions on Neural Networks and Learning Systems
Feihu HuangSheng-Jun Huang
Statistical Applications in Genetics and Molecular Biology
Anja Wille, Peter Bühlmann
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ariadna QuattoniTrevor Darrell
© 2021 Meta ULC. All rights reserved