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：我们研究了一类使用特征向量诱导变量的稀疏变分高斯过程方法中的点态估计与不确定性量化问题。针对重缩放布朗运动先验，我们从频率学派角度推导了点态置信集的尺寸和覆盖率的理论保证与局限性。当诱导变量数量足够多时，我们精确刻画了渐近频率学派覆盖率的特征，阐明了该变分方法产生的置信集在何种情形下保守、在何种情形下过度自信/具有误导性。我们通过数值实验验证了结果的适用性，并讨论了与其他常见高斯过程先验的联系。