Per-Family Error Rate Control for Gaussian Graphical Model via Knockoffs

• Activity Number: 80 - Graphical Models and Causal Inference
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Siliang Gong* and Qi Long and Weijie Su
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
• Keywords: Gaussian graphical model; Knockoffs; Multiple Testing

Abstract

Driven by many real applications including, but not limited to, estimation of biological pathways, the estimation of and inference for Gaussian Graphical Models (GGM) are fundamentally important and have attracted substantial research interest in the literature. However, it is still challenging to achieve overall error rate control when recovering the graph structures of GGM. In this paper, we propose a new multiple testing method for GGM using the knockoffs framework introduced by Barber and Candès. Our method is shown to control the overall finite-sample Per-Family Error Rate up to a probability error bound induced by the estimation errors of knockoff features. The performance of our method is evaluated in extensive numerical studies.