Speeding up Permutation Testing in Neuroimaging

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 $\alpha$-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 $\alpha$-threshold is also recovered faithfully, and is stable.Comment: NIPS 1

Contributions of anterior cingulate cortex and basolateral amygdala to decision confidence and learning under uncertainty.

The subjective sense of certainty, or confidence, in ambiguous sensory cues can alter the interpretation of reward feedback and facilitate learning. We trained rats to report the orientation of ambiguous visual stimuli according to a spatial stimulus-response rule that must be learned. Following choice, rats could wait a self-timed delay for reward or initiate a new trial. Waiting times increase with discrimination accuracy, demonstrating that this measure can be used as a proxy for confidence. Chemogenetic silencing of BLA shortens waiting times overall whereas ACC inhibition renders waiting times insensitive to confidence-modulating attributes of visual stimuli, suggesting contribution of ACC but not BLA to confidence computations. Subsequent reversal learning is enhanced by confidence. Both ACC and BLA inhibition block this enhancement but via differential adjustments in learning strategies and consistent use of learned rules. Altogether, we demonstrate dissociable roles for ACC and BLA in transmitting confidence and learning under uncertainty

A diel method of estimating gross primary production: 1. Validation with a realistic numerical model of Chesapeake Bay

Author Posting. © American Geophysical Union, 2018. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 123(11), (2018): 8411-8429, doi: 10.1029/2018JC014178.A method for estimating gross primary production (GPP) is presented and validated against a numerical model of Chesapeake Bay that includes realistic physical and biological forcing. The method statistically fits a photosynthesis‐irradiance response curve using the observed near‐surface time rate of change of dissolved oxygen and the incoming solar radiation, yielding estimates of the light‐saturated photosynthetic rate and the initial slope of the photosynthesis‐irradiance response curve. This allows estimation of GPP with 15‐day temporal resolution. The method is applied to the output from a numerical model that has high skill at reproducing both surface and near‐bottom dissolved oxygen variations observed in Chesapeake Bay in 2013. The rate of GPP predicted by the numerical model is known, as are the contributions from physical processes, allowing the proposed diel method to be rigorously assessed. At locations throughout the main stem of the Bay, the method accurately extracts the underlying rate of GPP, including pronounced seasonal variability and spatial variability. Errors associated with the method are primarily the result of contributions by the divergence in turbulent oxygen flux, which changes sign over the surface mixed layer. As a result, there is an optimal vertical location with minimal bias where application of the method is most accurate.This paper is the result of research funded in part by NOAA's U.S. Integrated Ocean Observing System (IOOS) Program Office as a subcontract to the Woods Hole Oceanographic Institution under award NA13NOS120139 to the Southeastern University Research Association. All of the model output, as well as both the CBIBS data (2010–2016) and the bottom oxygen data of Scully (2016b), are publicly available through the THREDDS server associated with the IOOS Coastal Modeling Testbed site: https://comt.ioos.us/projects/cb_hypoxia.2019-05-2