Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called \textit{Type II maximum likelihood} or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call \textit{Fully Bayesian Gaussian Process Regression} (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC) yielding a sampling-based approximation and 2) Variational Inference (VI) where the posterior over hyperparameters is approximated by a factorized Gaussian (mean-field) or a full-rank Gaussian accounting for correlations between hyperparameters. We analyze the predictive performance for fully Bayesian GPR on a range of benchmark data sets.
翻译:Gaussian 进程模型中的学习是通过调整平均值和共差函数的超参数来进行的。古典方法要求最大限度地增加得出固定点估计数的边际可能性(一种称为\ textit{Type II 最大可能性的方法 ) 或 ML-II 。 另一种学习程序是在我们称为\ textit{Fully Bayesian Gaussian 进程回归(GPR)的GPS的等级规格中,将后方数推至超参数。 这项工作考虑了两种棘手超参数后方数的近似方案:(1) 汉密尔顿·蒙特卡洛(HMHC)产生基于抽样的近似值,和(2) 推论(VI),即超参数的后方数被一个系数化的Gaussian(平均场)或一个全位的Gaussian计算超参数之间相互关系的计算法。我们在一系列基准数据集中分析了全巴伊西亚GPR的预测性能。