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.

Data fission: splitting a single data point

“…In some specific settings, data carving approaches may also offer a viable path forward. When the (fused or generalized) lasso is used to select the choice of knots, methods such as those described in Chen et al (2021), Duy andTakeuchi (2021), andHyun et al (2018) can be used to construct test and confidence intervals with valid post-selective distributions. Although tests constructed through these methodologies will likely have higher power than a data blurring approach due to conditioning on a smaller amount of information, the drawback of these approaches is that they offer the analyst very little flexibility during the selection stage.…”