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，它采用高斯过程作为先验，用于描述网络中每个变量在给定其父节点条件下的条件期望。该模型能以紧凑而灵活的方式描述连续联合分布，同时对变量间的依赖性施加最少的参数假设。对GPN进行贝叶斯结构学习需要计算网络图的后验，即使是在低维情况下，这一过程在计算上也是不可行的。本研究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。因此，该方法遵循贝叶斯范式，通过边际似然比较模型，并计算GPN特征的其后验概率。模拟研究表明，我们的方法在恢复网络的图结构方面优于现有最先进的算法，并能精确近似其后验分布。