Trade-offs of Linear Mixed Models in Genome-Wide Association Studies.

Motivated by empirical arguments that are well known from the genome-wide association studies (GWAS) literature, we study the statistical properties of linear mixed models (LMMs) applied to GWAS. First, we study the sensitivity of LMMs to the inclusion of a candidate single nucleotide polymorphism (SNP) in the kinship matrix, which is often done in practice to speed up computations. Our results shed light on the size of the error incurred by including a candidate SNP, providing a justification to this technique to trade off velocity against veracity.

Precision Lasso: accounting for correlations and linear dependencies in high-dimensional genomic data.

Motivation: Association studies to discover links between genetic markers and phenotypes are central to bioinformatics. Methods of regularized regression, such as variants of the Lasso, are popular for this task. Despite the good predictive performance of these methods in the average case, they suffer from unstable selections of correlated variables and inconsistent selections of linearly dependent variables.

Personalized regression enables sample-specific pan-cancer analysis.

Motivation: In many applications, inter-sample heterogeneity is crucial to understanding the complex biological processes under study. For example, in genomic analysis of cancers, each patient in a cohort may have a different driver mutation, making it difficult or impossible to identify causal mutations from an averaged view of the entire cohort. Unfortunately, many traditional methods for genomic analysis seek to estimate a single model which is shared by all samples in a population, ignoring this inter-sample heterogeneity entirely.

Variable selection in heterogeneous datasets: A truncated-rank sparse linear mixed model with applications to genome-wide association studies.

A fundamental and important challenge in modern datasets of ever increasing dimensionality is variable selection, which has taken on renewed interest recently due to the growth of biological and medical datasets with complex, non-i.i.d.

Variable Selection in Heterogeneous Datasets: A Truncated-rank Sparse Linear Mixed Model with Applications to Genome-wide Association Studies.

A fundamental and important challenge in modern datasets of ever increasing dimensionality is variable selection, which has taken on renewed interest recently due to the growth of biological and medical datasets with complex, non-i.i.d.