False Discovery Rate Control with Knockoffs and Accumulation Tests

In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are associated with the response, while controlling the false discovery rate (FDR) to ensure that our results are reliable and replicable. The knockoff filter is a variable selection procedure for linear regression, proven to control FDR exactly, by manufacturing knockoff variables designed to mimic the correlation structure found within the existing variables, leading to greater power than existing selection rules when searching for a highly sparse model. A related problem is that of ordered hypothesis testing, where we seek to find signals in an ordered list, such as in a path of increasing submodels. For this problem, we develop accumulation tests that run by accumulating an estimate of the number of false positives as we move down the list. This family of tests demonstrates a large increase in power by leveraging the information of the ordering. The knockoff filter is joint work with Emmanuel Candès, and the accumulation tests are joint work with Ang Li.

Event Topic

Nonlinear Algebra and Statistics (NLASTATS)