  In computational neuroscience, it is important to estimate well the
proportion of signal variance in the total variance of neural activity
measurements. This explainable variance measure helps neuroscientists assess
the adequacy of predictive models that describe how images are encoded in the
brain. Complicating the estimation problem are strong noise correlations, which
may confound the neural responses corresponding to the stimuli. If not properly
taken into account, the correlations could inflate the explainable variance
estimates and suggest false possible prediction accuracies. We propose a novel
method to estimate the explainable variance in functional MRI (fMRI) brain
activity measurements when there are strong correlations in the noise. Our
shuffle estimator is nonparametric, unbiased, and built upon the random effect
model reflecting the randomization in the fMRI data collection process.
Leveraging symmetries in the measurements, our estimator is obtained by
appropriately permuting the measurement vector in such a way that the noise
covariance structure is intact but the explainable variance is changed after
the permutation. This difference is then used to estimate the explainable
variance. We validate the properties of the proposed method in simulation
experiments. For the image-fMRI data, we show that the shuffle estimates can
explain the variation in prediction accuracy for voxels within the primary
visual cortex (V1) better than alternative parametric methods.
