This paper proposes an improved most likely heteroscedastic Gaussian process (MLHGP) algorithm to handle a kind of nonlinear regression problems involving input-dependent noise. The improved MLHGP follows the same learning scheme as the current algorithm by use of two Gaussian processes (GPs), with the first GP for recovering the unknown function and the second GP for modeling the input-dependent noise. Unlike the current MLHGP pursuing an empirical estimate of the noise level which is provably biased in most of local noise cases, the improved algorithm gives rise to an approximately unbiased estimate of the input-dependent noise. The approximately unbiased noise estimate is elicited from Bayesian residuals by the method of moments. As a by-product of this improvement, the expectation maximization (EM)-like procedure in the current MLHGP is avoided such that the improved algorithm requires only standard GP learnings to be performed twice. Four benchmark experiments, consisting of two synthetic cases and two real-world datasets, demonstrate that the improved MLHGP algorithm outperforms the current version not only in accuracy and stability, but also in computational efficiency.

中文翻译：

---

通过贝叶斯残差矩估计器改进最可能的异方差高斯过程回归

本文提出了一种改进的最可能异方差高斯过程（MLHGP）算法来处理一种涉及输入相关噪声的非线性回归问题。改进的 MLHGP 遵循与当前算法相同的学习方案，使用两个高斯过程 (GP)，第一个 GP 用于恢复未知函数，第二个 GP 用于对依赖于输入的噪声进行建模。与当前的 MLHGP 追求噪声水平的经验估计不同，该估计在大多数局部噪声情况下可证明是有偏差的，改进的算法产生了对输入相关噪声的近似无偏估计。近似无偏噪声估计是通过矩量法从贝叶斯残差导出的。作为这种改进的副产品，避免了当前 MLHGP 中的类似期望最大化 (EM) 的过程，因此改进的算法只需要执行两次标准的 GP 学习。由两个合成案例和两个真实世界数据集组成的四个基准实验表明，改进的 MLHGP 算法不仅在准确性和稳定性方面都优于当前版本，而且在计算效率方面也优于当前版本。