On the distribution of cross-validated Mahalanobis distances

TL;DR

This paper derives analytical formulas for the mean and covariance of cross-validated Mahalanobis distances, facilitating statistical inference and model comparison in neural representational similarity analysis using fMRI data.

Contribution

It provides the first analytical expressions for the distribution of cross-validated Mahalanobis distances, enabling normal approximation and improved statistical testing.

Findings

Allows statistical assessment of distance differences

Enables comparison of neural data to computational models

Facilitates inference in representational similarity analysis

Abstract

We present analytical expressions for the means and covariances of the sample distribution of the cross-validated Mahalanobis distance. This measure has proven to be especially useful in the context of representational similarity analysis (RSA) of neural activity patterns as measured by means of functional magnetic resonance imaging (fMRI). These expressions allow us to construct a normal approximation to the estimated distances, which in turn enables powerful inference on the measured statistics. Using the results, the difference between two distances can be statistically assessed, and the measured structure of the distances can be efficiently compared to predictions from computational models.