Gaussian Process-Gated Hierarchical Mixtures of Experts

In this paper, we propose novel Gaussian process-gated hierarchical mixtures of experts (GPHMEs) that are used for building gates and experts. Unlike in other mixtures of experts where the gating models are linear to the input, the gating functions of our model are inner nodes built with Gaussian processes based on random features that are non-linear and non-parametric. Further, the experts are also built with Gaussian processes and provide predictions that depend on test data. The optimization of the GPHMEs is carried out by variational inference. There are several advantages of the proposed GPHMEs. One is that they outperform tree-based HME benchmarks that partition the data in the input space. Another advantage is that they achieve good performance with reduced complexity. A third advantage of the GPHMEs is that they provide interpretability of deep Gaussian processes and more generally of deep Bayesian neural networks. Our GPHMEs demonstrate excellent performance for large-scale data sets even with quite modest sizes.