We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the correlated error, and the variance of the noise based on maximizing a marginal likelihood function. Our method involves suitably reducing the dimensionality of the hyperparameter space to simplify the estimation procedure to a univariate root-finding problem. Moreover, we derive bounds and asymptotes of the marginal likelihood function and its derivatives, which are useful to narrowing the initial range of the hyperparameter search. Using numerical examples, we demonstrate the computational advantages and robustness of the presented approach compared to traditional parameter optimization.
翻译:我们开发了一个计算程序,用添加噪声来估计半参数高斯进程回归模型的共差超参数。 也就是说, 所提出的方法可用于有效估计相关差错的差异, 以及以最大可能性函数为基础的噪音的差异。 我们的方法是适当减少超参数空间的维度, 以简化估算程序, 将其简化为单一的根调查问题。 此外, 我们获得边际概率函数及其衍生物的界限和静态, 这有助于缩小超参数搜索的初始范围。 我们用数字例子来展示所提出方法的计算优势和稳健性, 而不是传统的参数优化 。