Fast probabilistic whitening transformation for ultra-high dimensional genetic data

Statistical methods often make assumptions about independence between the samples or features of a dataset, yet correlation structure is ubiquitous in real data. In statistical genetics, correlation between regression summary statistics due to linkage disequilibrium (LD) between nearby variants complicates downstream analysis. Many methods use LD reference panels to account for this correlation. Whitening transformations comprise a family of methods to remove correlation structure, and are used implicitly by many common models. Here we propose a probabilistic model for data whitening, and propose parameter estimates and efficient algorithms to improve statistical and computational performance. In an application to impute z-statistics from unobserved genetic variants from a genome-wide association study of schizophrenia, the probabilistic whitening transformation, had the lowest mean square error while being up to an order of magnitude faster than other methods. Using this approach, we also identify tandem repeats that explain genetic regulatory signals for disease-relevant genes. Analyses are implemented in our novel open source R packages decorrelate and imputez.Author summary: Many statistical methods for analysis of regression summary statistics from genome-wide association statistics incorporate linkage disequilibrium matrices from a reference panel. Here, we examine whitening transformations, a general family of linear algebra operations that account for correlation structure. By examining the statistical properties and computational limitations of existing whitening transforms, we propose a novel approach to improve statistical performance and computational efficiency.