The Conditional Prediction Function: A Novel Technique to Control False
  Discovery Rate for Complex Models
Yushu Shi Michael Martens
In modern scientific research, the objective is often to identify which
variables are associated with an outcome among a large class of potential
predictors. This goal can be achieved by selecting variables in a manner that
controls the the false discovery rate (FDR), the proportion of irrelevant
predictors among the selections. Knockoff filtering is a cutting-edge approach
to variable selection that provides FDR control. Existing knockoff statistics
frequently employ linear models to assess relationships between features and
the response, but the linearity assumption is often violated in real world
applications. This may result in poor power to detect truly prognostic
variables. We introduce a knockoff statistic based on the conditional
prediction function (CPF), which can pair with state-of-art machine learning
predictive models, such as deep neural networks. The CPF statistics can capture
the nonlinear relationships between predictors and outcomes while also
accounting for correlation between features. We illustrate the capability of
the CPF statistics to provide superior power over common knockoff statistics
with continuous, categorical, and survival outcomes using repeated simulations.
Knockoff filtering with the CPF statistics is demonstrated using (1) a
residential building dataset to select predictors for the actual sales prices
and (2) the TCGA dataset to select genes that are correlated with disease
staging in lung cancer patients.