Predicting phenotypes from microarrays using amplified, initially marginal, eigenvector regression

Sufficient principal component regression for pattern discovery in transcriptomic data

Motivation

Methods for the 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.

Results

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.

Availability and implementation

Code and raw data are freely available at https://github.com/dajmcdon/suffpcr. Package documentation may be viewed at https://dajmcdon.github.io/suffpcr.

Contact

daniel@stat.ubc.ca.

Supplementary information

Supplementary data are available at Bioinformatics Advances online.

SMSSVD: SubMatrix Selection Singular Value Decomposition

Motivation

High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data analysis. Existing methods, aimed at signal reconstruction and deconvolution, in general, are either supervised, contain parameters that need to be estimated or present other types of ad hoc features. We here introduce SubMatrix Selection Singular Value Decomposition (SMSSVD), a parameter-free unsupervised signal decomposition and dimension reduction method, designed to reduce noise, adaptively for each low-rank-signal in a given data matrix, and represent the signals in the data in a way that enable unbiased exploratory analysis and reconstruction of multiple overlaid signals, including identifying groups of variables that drive different signals.

Results

The SMSSVD method produces a denoised signal decomposition from a given data matrix. It also guarantees orthogonality between signal components in a straightforward manner and it is designed to make automation possible. We illustrate SMSSVD by applying it to several real and synthetic datasets and compare its performance to golden standard methods like PCA (Principal Component Analysis) and SPC (Sparse Principal Components, using Lasso constraints). The SMSSVD is computationally efficient and despite being a parameter-free method, in general, outperforms existing statistical learning methods.

Availability and implementation

A Julia implementation of SMSSVD is openly available on GitHub (https://github.com/rasmushenningsson/SubMatrixSelectionSVD.jl).

Supplementary information

Supplementary data are available at Bioinformatics online.