加速神经影像学中的排列测试
Speeding up Permutation Testing in Neuroimaging
摘要：
多重假设检验是几乎所有神经影像学研究中的一个重要问题。为了纠正这种现象，我们需要一个可靠的估计家庭明智的错误率（FWER）。众所周知的Bonferroni校正方法虽然易于实现，但相当保守，并且由于其忽略了检验统计量之间的依赖性，因此可能大大降低研究的功效。另一方面，置换测试是一种针对给定的$α$阈值估计FWER的精确的非参数方法，但是对于可接受的低阈值，计算负担可能是过高的。在本文中，我们表明，置换测试实际上相当于填充一个非常大的矩阵${\bf P}$的列。通过分析该矩阵的谱，在一定条件下，我们发现${\bf P}$具有低秩和低方差的残差分解，这使得它适合于高度子采样的矩阵完备化方法，其阶数为$0.5\%$。基于这一观察，我们提出了一种新的排列测试方法，它提供了一个大的加速比，而不牺牲保真度的估计FWER。我们对四个不同的神经影像数据集的评估表明，计算加速因子大致$50\times$可以实现，同时恢复FWER分布达到非常高的精度。此外，我们表明，估计的$α$阈值也恢复忠实，是稳定的。
英文摘要：
Multiple hypothesis testing is a significant problem in nearly all neuroimaging studies. In order to correct for this phenomena, we require a reliable estimate of the Family-Wise Error Rate (FWER). The well known Bonferroni correction method, while simple to implement, is quite conservative, and can substantially under-power a study because it ignores dependencies between test statistics. Permutation testing, on the other hand, is an exact, non-parametric method of estimating the FWER for a given $α$-threshold, but for acceptably low thresholds the computational burden can be prohibitive. In this paper, we show that permutation testing in fact amounts to populating the columns of a very large matrix ${\bf P}$. By analyzing the spectrum of this matrix, under certain conditions, we see that ${\bf P}$ has a low-rank plus a low-variance residual decomposition which makes it suitable for highly sub--sampled --- on the order of $0.5\%$ --- matrix completion methods. Based on this observation, we propose a novel permutation testing methodology which offers a large speedup, without sacrificing the fidelity of the estimated FWER. Our evaluations on four different neuroimaging datasets show that a computational speedup factor of roughly $50\times$ can be achieved while recovering the FWER distribution up to very high accuracy. Further, we show that the estimated $α$-threshold is also recovered faithfully, and is stable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
