  Recent advances in neuroscientific experimental techniques have enabled us to
simultaneously record the activity of thousands of neurons across multiple
brain regions. This has led to a growing need for computational tools capable
of analyzing how task-relevant information is represented and communicated
between several brain regions. Partial information decompositions (PIDs) have
emerged as one such tool, quantifying how much unique, redundant and
synergistic information two or more brain regions carry about a task-relevant
message. However, computing PIDs is computationally challenging in practice,
and statistical issues such as the bias and variance of estimates remain
largely unexplored. In this paper, we propose a new method for efficiently
computing and estimating a PID definition on multivariate Gaussian
distributions. We show empirically that our method satisfies an intuitive
additivity property, and recovers the ground truth in a battery of canonical
examples, even at high dimensionality. We also propose and evaluate, for the
first time, a method to correct the bias in PID estimates at finite sample
sizes. Finally, we demonstrate that our Gaussian PID effectively characterizes
inter-areal interactions in the mouse brain, revealing higher redundancy
between visual areas when a stimulus is behaviorally relevant.
