A Bayesian Take on Gaussian Process Networks
This work addresses a computational bottleneck for researchers in Bayesian machine learning and graphical models, offering an incremental improvement over existing methods.
The paper tackles the computationally infeasible problem of Bayesian structure learning for Gaussian Process Networks by implementing Monte Carlo and Markov Chain Monte Carlo methods to sample from the posterior distribution of network structures. Simulation studies show that the method outperforms state-of-the-art algorithms in recovering the graphical structure and provides an accurate approximation of its posterior distribution.
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 the description of 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.