We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and limitations for the frequentist coverage of the resulting variational credible sets. We also derive sufficient and necessary lower bounds for the number of inducing variables required to achieve minimax posterior contraction rates. The implications of these results are demonstrated for different choices of priors. In a numerical analysis we consider a wider range of inducing variable methods and observe similar phenomena beyond the scope of our theoretical findings.

翻译：我们研究了变分稀疏高斯过程回归模型的频率学派保证。在理论分析中，我们重点关注以谱特征作为诱导变量的变分方法。我们推导了所得变分置信集的频率学派覆盖率的保证与局限性。我们还推导了为实现极小极大后验收缩速率所需诱导变量数量的充分且必要下界。这些结果对不同先验选择的影响得到了阐明。在数值分析中，我们考虑了更广泛的诱导变量方法，并在超出我们理论发现范围的场景中观察到类似现象。