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Differential co-expression analysis has been widely applied by scientists inunderstanding the biological mechanisms of diseases. However, the unknowndifferential patterns are often complicated; thus, models based on simplifiedparametric assumptions can be ineffective in identifying the differences.Meanwhile, the gene expression data involved in such analysis are in extremelyhigh dimensions by nature, whose correlation matrices may not even becomputable. Such a large scale seriously limits the application of mostwell-studied statistical methods. This paper introduces a simple yet powerfulapproach to the differential correlation analysis problem called compressedspectral screening. By leveraging spectral structures and random samplingtechniques, our approach could achieve a highly accurate screening of featureswith complicated differential patterns while maintaining the scalability toanalyze correlation matrices of $10^4$--$10^5$ variables within a few minuteson a standard personal computer. We have applied this screening approach incomparing a TCGA data set about Glioblastoma with normal subjects. Our analysissuccessfully identifies multiple functional modules of genes that exhibitdifferent co-expression patterns. The findings reveal new insights aboutGlioblastoma's evolving mechanism. The validity of our approach is alsojustified by a theoretical analysis, showing that the compressed spectralanalysis can achieve variable screening consistency.

Compressed spectral screening for large-scale differential correlation analysis with application in selecting Glioblastoma gene modules