Heterogeneity adjustment with applications to graphical model inference

Jianqing Fan, Han Liu, Weichen Wang, Ziwei Zhu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3908-3952
Number of pages45
JournalElectronic Journal of Statistics
Issue number2
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Batch effect
  • Brain image network
  • Multiple sourcing
  • Principal component analysis
  • Semiparametric factor model


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