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。

从时移信号中稳健且高度可扩展地估计方向耦合

Robust and highly scalable estimation of directional couplings from  time-shifted signals

Current methods for learning graphical models with latent variables and a
fixed structure estimate optimal values for the model parameters. Whereas this
approach usually produces overfitting and suboptimal generalization
performance, carrying out the Bayesian program of computing the full posterior
distributions over the parameters remains a difficult problem. Moreover,
learning the structure of models with latent variables, for which the Bayesian
approach is crucial, is yet a harder problem. In this paper I present the
Variational Bayes framework, which provides a solution to these problems. This
approach approximates full posterior distributions over model parameters and
structures, as well as latent variables, in an analytical manner without
resorting to sampling methods. Unlike in the Laplace approximation, these
posteriors are generally non-Gaussian and no Hessian needs to be computed. The
resulting algorithm generalizes the standard Expectation Maximization
algorithm, and its convergence is guaranteed. I demonstrate that this algorithm
can be applied to a large class of models in several domains, including
unsupervised clustering and blind source separation.

本文提出了变分贝叶斯 (Variational Bayes) 框架，通过解决概率图模型中潜在变量及其结构计算的问题，避免了因参数而导致过拟合和子最优泛化表现的通常方法，同时证明了该算法能成功应用于无监督聚类、盲源分离等模型。