Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive for larger datasets. We propose a Bayesian Quadrature scheme to make this marginalisation more efficient and thereby more practical. Through use of the maximum mean discrepancies between distributions, we define a kernel over kernels that captures invariances between Spectral Mixture (SM) Kernels. Kernel samples are selected by generalising an information-theoretic acquisition function for warped Bayesian Quadrature. We show that our framework achieves more accurate predictions with better calibrated uncertainty than state-of-the-art baselines, especially when given limited (wall-clock) time budgets.

翻译：对高斯过程核函数族进行边缘化可产生具有良好校准不确定度估计的灵活模型类。现有方法需要计算大量核函数的似然值，导致其在较大数据集上代价过高。我们提出一种贝叶斯求积方案，旨在提高这种边缘化过程的效率，从而使其更具实用性。通过利用分布之间的最大均值差异，我们定义了一种核函数上的核，该核能够捕捉谱混合(Spectral Mixture, SM)核之间的不变性。核样本的选择通过推广一种用于扭曲贝叶斯求积的信息论采集函数来实现。实验表明，我们的框架比现有最先进基线方法能实现更准确的预测，并具有更优校准的不确定度，尤其是在有限的(挂钟)时间预算约束下表现显著。