Journal
BIOMETRIKA
Volume 104, Issue 4, Pages 755-770Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asx049
Keywords
Gaussian graphical model; Gene regulatory network; High dimensionality; Precision matrix; Sign consistency
Funding
- National Key Basic Research Project of China
- National Natural Science Foundation of China
- Recruitment Program of Global Youth Experts of China
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Biological networks often change under different environmental and genetic conditions. In this paper, we model network change as the difference of two precision matrices and propose a novel loss function called the D-trace loss, which allows us to directly estimate the precision matrix difference without attempting to estimate the precision matrices themselves. Under a new irrepresentability condition, we show that the D-trace loss function with the lasso penalty can yield consistent estimators in high-dimensional settings if the difference network is sparse. A very efficient algorithm is developed based on the alternating direction method of multipliers to minimize the penalized loss function. Simulation studies and a real-data analysis show that the proposed method outperforms other methods.
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