论文标题
高斯过程回归中稀疏光谱变异近似的不确定性定量
Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression
论文作者
论文摘要
我们研究了稀疏高斯过程回归模型的频繁保证。在理论分析中，我们关注具有光谱特征作为诱导变量的变异方法。我们得出保证和局限性，以实现由此产生的可靠集合的频繁覆盖范围。我们还为实现最小值后收缩率所需的诱导变量数量提供了足够和必要的下限。这些结果的含义是针对先验选择的不同选择。在数值分析中，我们考虑了更广泛的诱导可变方法，并观察到我们理论发现范围之外的类似现象。
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.
