IEEE Trans Neural Netw Learn Syst. 2014 Nov;25(11):1991-2003. doi: 10.1109/TNNLS.2014.2301951.
Standard Gaussian process regression (GPR) assumes constant noise power throughout the input space and stationarity when combined with the squared exponential covariance function. This can be unrealistic and too restrictive for many real-world problems. Nonstationarity can be achieved by specific covariance functions, though prior knowledge about this nonstationarity can be difficult to obtain. On the other hand, the homoscedastic assumption is needed to allow GPR inference to be tractable. In this paper, we present a divisive GPR model which performs nonstationary regression under heteroscedastic noise using the pointwise division of two nonparametric latent functions. As the inference on the model is not analytically tractable, we propose a variational posterior approximation using expectation propagation (EP) which allows for accurate inference at reduced cost. We have also made a Markov chain Monte Carlo implementation with elliptical slice sampling to assess the quality of the EP approximation. Experiments support the usefulness of the proposed approach.
标准高斯过程回归（GPR）假设在输入空间中噪声功率保持不变，并且在与平方指数协方差函数结合使用时具有平稳性。对于许多实际问题来说，这可能是不现实和过于严格的。通过特定的协方差函数可以实现非平稳性，尽管关于这种非平稳性的先验知识可能很难获得。另一方面，需要同方差假设才能使 GPR 推断具有可处理性。在本文中，我们提出了一种分裂的 GPR 模型，该模型使用两个非参数潜在函数的逐点划分在异方差噪声下执行非平稳回归。由于对模型的推理不能进行解析处理，因此我们提出了一种使用期望传播（EP）的变分后验近似，该近似允许以降低的成本进行准确的推理。我们还使用椭圆切片抽样实现了马尔可夫链蒙特卡罗（MCMC），以评估 EP 近似的质量。实验支持了所提出方法的有用性。
