Integrative Learning of Structured High-Dimensional Data from Multiple Datasets

TL;DR

This paper introduces a novel integrative learning method for high-dimensional data from multiple datasets, leveraging known feature graphs to improve feature selection, especially when signals are weak or heterogeneous across datasets.

Contribution

The proposed approach effectively combines prior feature graph information to enhance signal detection and address heterogeneity, outperforming existing methods.

Findings

Method improves detection of weak signals in heterogeneous data

Theoretical analysis confirms consistency and robustness

Application to gene expression data demonstrates practical advantages

Abstract

Integrative learning of multiple datasets has the potential to mitigate the challenge of small $n$ and large $p$ that is often encountered in analysis of big biomedical data such as genomics data. Detection of weak yet important signals can be enhanced by jointly selecting features for all datasets. However, the set of important features may not always be the same across all datasets. Although some existing integrative learning methods allow heterogeneous sparsity structure where a subset of datasets can have zero coefficients for some selected features, they tend to yield reduced efficiency, reinstating the problem of losing weak important signals. We propose a new integrative learning approach which can not only aggregate important signals well in homogeneous sparsity structure, but also substantially alleviate the problem of losing weak important signals in heterogeneous sparsity structure. Our approach exploits a priori known graphical structure of features and encourages joint selection of features that are connected in the graph. Integrating such prior information over multiple datasets enhances the power, while also accounting for the heterogeneity across datasets. Theoretical properties of the proposed method are investigated. We also demonstrate the limitations of existing approaches and the superiority of our method using a simulation study and analysis of gene expression data from ADNI.