We study pointwise estimation and uncertainty quantification for a sparse variational Gaussian process method with eigenvector inducing variables. For a rescaled Brownian motion prior, we derive theoretical guarantees and limitations for the frequentist size and coverage of pointwise credible sets. For sufficiently many inducing variables, we precisely characterize the asymptotic frequentist coverage, deducing when credible sets from this variational method are conservative and when overconfident/misleading. We numerically illustrate the applicability of our results and discuss connections with other common Gaussian process priors.

翻译：我们研究了具有特征向量诱导变量的稀疏变分高斯过程方法的点态估计与不确定性量化。针对重缩放布朗运动先验，我们推导了点态可信集的频率学派尺度与覆盖范围的理论保证及其局限性。对于足够多的诱导变量，我们精确刻画了渐近频率学派覆盖范围，揭示了该变分方法所生成的可信集何时保守、何时过度自信/具有误导性。我们通过数值实验展示了所得结果的适用性，并讨论了与其他常见高斯过程先验的联系。