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.

使用变分贝叶斯框架，我们通过边际化延迟的不确定性，提供了对网络节点之间的定向耦合估计问题的解决方案。通过使用混合 - VI 方案，我们能够对测量参数的后验分布进行估计，同时使用基于梯度的高度可扩展的 VI 估计耦合的条件后验分布。在我们的基准实验中，我们展示了网络能够可靠且保守地估计耦合，明显优于回归 DCM 等相似方法。