论文标题
使用Martingales进行不确定的高斯流程的不确定性定量
Uncertainty quantification using martingales for misspecified Gaussian processes
论文作者
论文摘要
我们解决了在拼写错误的先验下的高斯工艺（GP）的不确定性定量，并注视着贝叶斯优化（BO）。 GP在BO中广泛使用，因为它们很容易根据后不确定性带进行探索。但是，这种便利性是以鲁棒性为代价的：实践中遇到的典型功能不太可能是从数据科学家的先前提取的，在这种情况下，不确定性估计可能会产生误导，并且由此产生的探索可能是最佳的。我们提出了一种常见的GP/BO不确定性定量方法。我们将GP框架用作工作模型，但不假定先验的正确性。相反，我们使用Martingale技术为未知函数构建了一个置信序列（CS）。实现鲁棒性是有必要的成本：如果先验是正确的，则后GP频段比我们的CS窄。然而，当先验是错误的情况下，就BO的覆盖范围和实用程序而言，我们的CS在统计上有效，并且在经验上优于标准GP方法。此外，我们证明了有动力的可能性为模型错误指定提供了鲁棒性。
We address uncertainty quantification for Gaussian processes (GPs) under misspecified priors, with an eye towards Bayesian Optimization (BO). GPs are widely used in BO because they easily enable exploration based on posterior uncertainty bands. However, this convenience comes at the cost of robustness: a typical function encountered in practice is unlikely to have been drawn from the data scientist's prior, in which case uncertainty estimates can be misleading, and the resulting exploration can be suboptimal. We present a frequentist approach to GP/BO uncertainty quantification. We utilize the GP framework as a working model, but do not assume correctness of the prior. We instead construct a confidence sequence (CS) for the unknown function using martingale techniques. There is a necessary cost to achieving robustness: if the prior was correct, posterior GP bands are narrower than our CS. Nevertheless, when the prior is wrong, our CS is statistically valid and empirically outperforms standard GP methods, in terms of both coverage and utility for BO. Additionally, we demonstrate that powered likelihoods provide robustness against model misspecification.
