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.

本文研究高斯过程网络 (GPNs) 的贝叶斯结构学习问题，提出基于蒙特卡罗和马尔可夫链蒙特卡罗方法的网络结构后验分布抽样算法，并在模拟实验中证明该方法在恢复网络图形结构和提供准确后验分布方面优于现有算法。

高斯过程网络的贝叶斯方法