Electronic Journal of Statistics

Heterogeneity adjustment with applications to graphical model inference

Jianqing Fan, Han Liu, Weichen Wang, and Ziwei Zhu

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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.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 3908-3952.

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

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Multiple sourcing batch effect semiparametric factor model principal component analysis brain image network

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Fan, Jianqing; Liu, Han; Wang, Weichen; Zhu, Ziwei. Heterogeneity adjustment with applications to graphical model inference. Electron. J. Statist. 12 (2018), no. 2, 3908--3952. doi:10.1214/18-EJS1466. https://projecteuclid.org/euclid.ejs/1543979030

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