Heterogeneity Adjustment with Applications to Graphical Model Inference

TL;DR

This paper introduces ALPHA, a comprehensive framework for modeling, estimating, and adjusting heterogeneity in aggregated datasets, improving inference accuracy in high-dimensional graphical models and other applications.

Contribution

The paper proposes a novel, theoretically justified framework called ALPHA for heterogeneity adjustment, incorporating covariates and leveraging high-dimensional properties.

Findings

ALPHA effectively removes batch effects and biases.

The framework improves precision matrix estimation in graphical models.

Numerical studies confirm the method's efficacy on synthetic and real data.

Abstract

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 biases of 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 large 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.