More powerful selective inference for the graph fused lasso

TL;DR

This paper introduces a new selective inference method for the graph fused lasso that controls Type I error and offers higher power, demonstrated through simulations and real-world datasets on public health metrics.

Contribution

It proposes a novel test for differences in connected components estimated by the graph fused lasso that controls selective Type I error with less conditioning, increasing power.

Findings

More discoveries in simulation studies.

Higher power compared to existing methods.

Effective on real-world public health data.

Abstract

The graph fused lasso -- which includes as a special case the one-dimensional fused lasso -- is widely used to reconstruct signals that are piecewise constant on a graph, meaning that nodes connected by an edge tend to have identical values. We consider testing for a difference in the means of two connected components estimated using the graph fused lasso. A naive procedure such as a z-test for a difference in means will not control the selective Type I error, since the hypothesis that we are testing is itself a function of the data. In this work, we propose a new test for this task that controls the selective Type I error, and conditions on less information than existing approaches, leading to substantially higher power. We illustrate our approach in simulation and on datasets of drug overdose death rates and teenage birth rates in the contiguous United States. Our approach yields more discoveries on both datasets.