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Recent advances in neuroscientific experimental techniques have enabled us tosimultaneously record the activity of thousands of neurons across multiplebrain regions. This has led to a growing need for computational tools capableof analyzing how task-relevant information is represented and communicatedbetween several brain regions. Partial information decompositions (PIDs) haveemerged as one such tool, quantifying how much unique, redundant andsynergistic information two or more brain regions carry about a task-relevantmessage. However, computing PIDs is computationally challenging in practice,and statistical issues such as the bias and variance of estimates remainlargely unexplored. In this paper, we propose a new method for efficientlycomputing and estimating a PID definition on multivariate Gaussiandistributions. We show empirically that our method satisfies an intuitiveadditivity property, and recovers the ground truth in a battery of canonicalexamples, even at high dimensionality. We also propose and evaluate, for thefirst time, a method to correct the bias in PID estimates at finite samplesizes. Finally, we demonstrate that our Gaussian PID effectively characterizesinter-areal interactions in the mouse brain, revealing higher redundancybetween visual areas when a stimulus is behaviorally relevant.

Gaussian Partial Information Decomposition: Bias Correction and Application to High-dimensional Data