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.

摘要

图融合套索（包括一维融合套索的特殊情况）广泛用于重建图上分段常数的信号，这意味着由边连接的节点往往具有相同的值。我们考虑测试使用图融合套索估计的两个连接分量的均值差异。简单的过程，例如z- 均值差异检验不会控制选择性 I 类错误，因为我们正在检验的假设本身就是数据的函数。在这项工作中，我们为此任务提出了一种新的测试，该测试控制选择性 I 型错误，并且条件信息比现有方法更少，从而获得更高的功效。我们通过模拟以及美国本土药物过量死亡率和青少年出生率的数据集来说明我们的方法。我们的方法在这两个数据集上产生了更多发现。本文的补充材料可在线获取。