The estimation of directed couplings between the nodes of a network from indirect measurements is a central methodological challenge in scientific fields such as neuroscience, systems biology and economics. Unfortunately, the problem is generally ill-posed due to the possible presence of unknown delays in the measurements. In this paper, we offer a solution of this problem by using a variational Bayes framework, where the uncertainty over the delays is marginalized in order to obtain conservative coupling estimates. To overcome the well-known overconfidence of classical variational methods, we use a hybrid-VI scheme where the (possibly flat or multimodal) posterior over the measurement parameters is estimated using a forward KL loss while the (nearly convex) conditional posterior over the couplings is estimated using the highly scalable gradient-based VI. In our ground-truth experiments, we show that the network provides reliable and conservative estimates of the couplings, greatly outperforming similar methods such as regression DCM.

翻译：从间接测量中估计网络节点间的定向耦合是神经科学、系统生物学和经济学等科学领域的核心方法论挑战。不幸的是，由于测量中可能存在未知延迟，该问题通常是病态的。在本文中，我们通过使用变分贝叶斯框架来解决这个问题，其中延迟的不确定性被边缘化，以获得保守的耦合估计。为了克服经典变分方法众所周知的过度自信问题，我们采用了一种混合变分推断方案：其中测量参数的（可能平坦或多峰的）后验使用前向KL损失进行估计，而耦合的（近乎凸的）条件后验则使用高度可扩展的基于梯度的变分推断进行估计。在我们的真实数据实验中，我们表明该网络能够提供可靠且保守的耦合估计，其性能大大超越了回归DCM等类似方法。