Heterogeneity adjustment with applications to graphical model inference

Jianqing Fan Han Liu Weichen Wang Ziwei Zhu

Statistics Theory and Methods mathscidoc:1912.43412

Electronic Journal of Statistics, 12, (2), 3908-3952, 2018
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
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  title={Heterogeneity adjustment with applications to graphical model inference},
  author={Jianqing Fan, Han Liu, Weichen Wang, and Ziwei Zhu},
  booktitle={Electronic Journal of Statistics},
Jianqing Fan, Han Liu, Weichen Wang, and Ziwei Zhu. Heterogeneity adjustment with applications to graphical model inference. 2018. Vol. 12. In Electronic Journal of Statistics. pp.3908-3952. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114251574467972.
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