Sufficient principal component regression for pattern discovery in transcriptomic data

Abstract: Methods for global measurement of transcript abundance such as microarrays and RNA-Seq generate datasets in which the number of measured features far exceeds the number of observations. Extracting biologically meaningful and experimentally tractable insights from such data therefore requires high-dimensional prediction. Existing sparse linear approaches to this challenge have been stunningly successful, but some important issues remain. These methods can fail to select the correct features, predict poorly relative to non-sparse alternatives, or ignore any unknown grouping structures for the features. We propose a method called SuffPCR that yields improved predictions in high-dimensional tasks including regression and classification, especially in the typical context of omics with correlated features. SuffPCR first estimates sparse principal components and then estimates a linear model on the recovered subspace. Because the estimated subspace is sparse in the features, the resulting predictions will depend on only a small subset of genes. SuffPCR works well on a variety of simulated and experimental transcriptomic data, performing nearly optimally when the model assumptions are satisfied. We also demonstrate near-optimal theoretical guarantees.