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.
翻译:螺纹引信 弧索 -- -- 包括单维引信 弧索 -- -- 被广泛用于重建在图形上成份恒定的信号,这意味着边缘连接的节点往往具有相同的值。我们考虑测试使用图形引信弧索估计的两个连接部件的不同手段。一个天真的程序,例如用Z测试来测量手段的差异,无法控制选择性的I型错误,因为我们测试的假设本身就是数据的一个函数。在这项工作中,我们提议对这一任务进行新的测试,以控制选择性的I型错误,以及信息比现有方法少的条件,从而导致更强大的能量。我们举例说明了我们在模拟中的方法,以及美国毗连地区吸毒过量死亡率和青少年出生率的数据集。我们的方法在这两个数据集上都产生了更多的发现。