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.

翻译：近年来神经科学实验技术的进步使我们能够同时记录跨多个脑区数千个神经元的活动。这引发了对能够分析任务相关信息如何在多个脑区间表征与传递的计算工具的迫切需求。部分信息分解（PIDs）作为一种此类工具应运而生，可量化两个或多个脑区携带关于任务相关信息的独有、冗余与协同信息量。然而，实际计算PIDs面临巨大挑战，且估计量的偏差与方差等统计问题尚未得到充分探索。本文提出一种新方法，用于高效计算和估计多变量高斯分布上的PID定义。经验表明，我们的方法满足直观的可加性属性，并在高维条件下仍能通过一系列典范示例恢复真实值。我们首次提出并评估了一种在有限样本量下校正PID估计偏差的方法。最后，我们证明高斯PID能有效表征小鼠脑内跨脑区相互作用，揭示当刺激具有行为相关性时视觉区之间呈现更高的冗余性。