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2018 Heterogeneity adjustment with applications to graphical model inference
Jianqing Fan, Han Liu, Weichen Wang, Ziwei Zhu
Electron. J. Statist. 12(2): 3908-3952 (2018). DOI: 10.1214/18-EJS1466


Heterogeneity is an unwanted variation when analyzing aggregated datasets from multiple sources. Though different methods have been proposed for heterogeneity adjustment, no systematic theory exists to justify these methods. In this work, we propose a generic framework named ALPHA (short for Adaptive Low-rank Principal Heterogeneity Adjustment) to model, estimate, and adjust heterogeneity from the original data. Once the heterogeneity is adjusted, we are able to remove the batch effects and to enhance the inferential power by aggregating the homogeneous residuals from multiple sources. Under a pervasive assumption that the latent heterogeneity factors simultaneously affect a fraction of observed variables, we provide a rigorous theory to justify the proposed framework. Our framework also allows the incorporation of informative covariates and appeals to the ‘Bless of Dimensionality’. As an illustrative application of this generic framework, we consider a problem of estimating high-dimensional precision matrix for graphical model inference based on multiple datasets. We also provide thorough numerical studies on both synthetic datasets and a brain imaging dataset to demonstrate the efficacy of the developed theory and methods.


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Jianqing Fan. Han Liu. Weichen Wang. Ziwei Zhu. "Heterogeneity adjustment with applications to graphical model inference." Electron. J. Statist. 12 (2) 3908 - 3952, 2018.


Received: 1 September 2017; Published: 2018
First available in Project Euclid: 5 December 2018

zbMATH: 07003233
MathSciNet: MR3883140
Digital Object Identifier: 10.1214/18-EJS1466


Vol.12 • No. 2 • 2018
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