Model selection for high dimensional data, with application towards genetics

The main goal of this project is the development of efficient methods for identifying predictors in large data bases, with the specific emphasis on identifying causal mutations and building predictive models based  on  Genome Wide Association Studies (GWAS).

For this aim we will theoretically investigate and expand the Sorted L-One Penalized Estimator (SLOPE) and its adaptive Bayesian version (ABSLOPE).

Specifically, we will:identify the conditions under which both methods asymptotically control the False Discovery Rate and are asymptotically optimal with respect to estimation and prediction properties.

We expect that ABSLOPE will allow to combine good model selection, estimation and prediction properties under a wide range of scenarios, including those with highly correlated predictors.develop mixed linear models appropriate for GWAS, where individuals are correlated due to the polygenic background, and extend ABSLOPE to identify  major genes based on such mixed models.develop efficient optimization algorithms for solving the SLOPE optimization problem, which will facilitate application of SLOPE and ABSLOPE for huge genetic data bases.Our results will expand the mathematical understanding of high dimensional statistics, and also provide a bridge, through  open source software, between the theoretical results and the practitioners.

The application for GWAS  has a potential to have a huge impact on many different fields like biology, psychology, social science, and many more.