Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance matrix. To circumvent this, mixtures of Gaussian process experts have been considered where data points are assigned to independent experts, reducing the complexity by allowing inference based on smaller, local covariance matrices. Moreover, mixtures of Gaussian process experts substantially enrich the model's flexibility, allowing for behaviors such as non-stationarity, heteroscedasticity, and discontinuities. In this work, we construct a novel inference approach based on nested sequential Monte Carlo samplers to simultaneously infer both the gating network and Gaussian process expert parameters. This greatly improves inference compared to importance sampling, particularly in settings when a stationary Gaussian process is inappropriate, while still being thoroughly parallelizable.

翻译：高斯过程是许多灵活的统计与机器学习模型的核心组成部分。然而，由于需要求逆并存储完整的协方差矩阵，其计算复杂度为立方阶且内存占用较高。为解决这一问题，研究者提出了高斯过程专家混合模型，该模型将数据点分配给独立的专家，通过基于更小的局部协方差矩阵进行推断来降低复杂度。此外，高斯过程专家混合模型显著增强了模型的灵活性，能够捕捉非平稳性、异方差性及不连续性等复杂特性。本文提出了一种基于嵌套序列蒙特卡洛采样器的新型推断方法，可同时推断门控网络与高斯过程专家参数。与重要性采样相比，该方法显著提升了推断效果，尤其适用于平稳高斯过程不适用的场景，同时仍具备高度的可并行性。