Model-X conditional knockoffs and conditional randomization tests using Gaussian graphical models

1983 

Contributed Abstract 

Paper 

Dongming Huang (1), Lucas Janson (2)

(1) National University of Singapore, Singapore, (2) Harvard University, Cambridge, MA, USA

Lucas Janson  
Harvard University

Dongming Huang  
National University of Singapore

Dongming Huang  
National University of Singapore

The model-X framework provides provable non-asymptotical error control on variable selection and conditional independence testing. It has no restrictions or assumptions on the dimensionality of the data or the conditional distribution of the response given the covariates. To relax the requirement of the model-X framework that the distribution of the covariate samples is precisely known, we proposed to construct knockoffs by conditioning on sufficient statistics when the distribution is known up to a parametric model with as many as Ω(np) parameters, where p is the dimension and n is the number of covariate samples (including unlabeled samples if available). We demonstrate how this idea can be implemented in Gaussian graphical models and show the new approach remains powerful under the weaker assumption. We will discuss how such conditioning can be extended to constructing a conditional randomization test for testing conditional independence between the response and a subset of the covariates.

variable selection|knockoff|model-X|Gaussian graphical model|randomization test|goodness-of-fit test

IMS

Statistical Methodology