The shape of neural dependence

The product-moment correlation coefficient is often viewed as a natural measure of dependence. However, this equivalence applies only in the context of elliptical distributions, most commonly the multivariate gaussian, where linear correlation indeed sufficiently describes the underlying dependence structure. Should the true probability distributions deviate from those with elliptical contours, linear correlation may convey misleading information on the actual underlying dependencies. It is often the case that probability distributions other than the gaussian distribution are necessary to properly capture the stochastic nature of single neurons, which as a consequence greatly complicates the construction of a flexible model of covariance. We show how arbitrary probability densities can be coupled to allow greater flexibility in the construction of multivariate neural population models.