Speeding up Permutation Testing in Neuroimaging

By Chris Hinrichs, Vamsi Krishna Ithapu, Qinyuan Sun, Sterling C. Johnson, Vikas Singh. 2013

7 citations recorded by the source corpus.

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 P. By analyzing the spectrum of this matrix, under certain conditions, we see that 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× 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.

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Citations in the corpus

Interpreting support vector machine models for multivariate group wise analysis in neuroimaging (2015, neutral): “Recent work by the authors of (Hinrichs et al., 2013) might offer an insight into analytically modelling these distributions.”
Faster permutation inference in brain imaging (2016, background): “While the rank can be recovered through the introduction of random noise with similar moments (Hinrichs et al., 2013), there is no guarantee that it will possess the same spatial structure that would preserve the distribution of spatial statistics used in imaging.”
Fast Random Integer Generation in an Interval (2018, background): “found that the computational burden due to random permutations can be prohibitive [15].”