GRIA: Graphical Regularization for Integrative Analysis.

Integrative analysis jointly analyzes multiple data sets to overcome curse of dimensionality. It can detect important but weak signals by jointly selecting features for all data sets, but unfortunately the sets of important features are not always the same for all data sets. Variations which allows heterogeneous sparsity structure-a subset of data sets can have a zero coefficient for a selected feature-have been proposed, but it compromises the effect of integrative analysis recalling the problem of losing weak important signals. We propose a new integrative analysis approach which not only aggregates weak important signals well in homogeneity setting but also substantially alleviates the problem of losing weak important signals in heterogeneity setting. Our approach exploits a priori known graphical structure of features by forcing joint selection of adjacent features, and integrating such information over multiple data sets can increase the power while taking into account the heterogeneity across data sets. We confirm the problem of existing approaches and demonstrate the superiority of our method through a simulation study and an application to gene expression data from ADNI.