Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows describing continuous joint distributions in a compact but flexible manner with minimal parametric assumptions on the dependencies between variables. Bayesian structure learning of GPNs requires computing the posterior over graphs of the network and is computationally infeasible even in low dimensions. This work implements Monte Carlo and Markov Chain Monte Carlo methods to sample from the posterior distribution of network structures. As such, the approach follows the Bayesian paradigm, comparing models via their marginal likelihood and computing the posterior probability of the GPN features. Simulation studies show that our method outperforms state-of-the-art algorithms in recovering the graphical structure of the network and provides an accurate approximation of its posterior distribution.

翻译：高斯过程网络（GPNs）是一类有向图模型，它利用高斯过程作为每个变量在其父节点条件下条件期望的先验分布。该模型能以紧凑但灵活的方式描述连续联合分布，且对变量间依赖关系的参数假设要求极低。GPN的贝叶斯结构学习需要计算网络图的后验分布，即使是在低维情况下，该计算也面临不可行性。本文采用蒙特卡洛和马尔可夫链蒙特卡洛方法，从网络结构的后验分布中采样。该方法遵循贝叶斯范式，通过边际似然比较模型，并计算GPN特征的后验概率。仿真研究表明，我们的方法在图结构恢复方面优于当前最优算法，并能精确近似其后验分布。