More Powerful Selective Inference for the Graph Fused Lasso

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. Supplementary materials for this article are available online.

KEYWORDS:

• Changepoint detection
• Hypothesis testing
• Penalized regression
• Piecewise constant

Supplementary Materials

The supplementary material contains proofs, technical details, and additional simulation results. [Online].

Disclosure Statement

The authors report there are no competing interests to declare.

Acknowledgments

We thank the authors of Le Duy and Takeuchi (2021) for providing us with their software implementation.

Additional information

Funding

This work was partially supported by National Institutes of Health grants [R01EB026908, R01DA047869] and a Simons Investigator Award to D.W.