The Gaussian process (GP) is a Bayesian nonparametric paradigm that is widely adopted for uncertainty quantification (UQ) in a number of safety-critical applications, including robotics, healthcare, as well as surveillance. The consistency of the resulting uncertainty values however, hinges on the premise that the learning function conforms to the properties specified by the GP model, such as smoothness, periodicity and more, which may not be satisfied in practice, especially with data arriving on the fly. To combat against such model mis-specification, we propose to wed the GP with the prevailing conformal prediction (CP), a distribution-free post-processing framework that produces it prediction sets with a provably valid coverage under the sole assumption of data exchangeability. However, this assumption is usually violated in the online setting, where a prediction set is sought before revealing the true label. To ensure long-term coverage guarantee, we will adaptively set the key threshold parameter based on the feedback whether the true label falls inside the prediction set. Numerical results demonstrate the merits of the online GP-CP approach relative to existing alternatives in the long-term coverage performance.

翻译：高斯过程（GP）是一种贝叶斯非参数范式，广泛应用于机器人、医疗保健及监控等安全关键领域的不确定性量化（UQ）。然而，所得不确定性值的可靠性依赖于学习函数符合GP模型所指定的性质（如平滑性、周期性等）这一前提，在实际应用中，特别是在数据动态到达的场景下，这一前提往往无法满足。为应对此类模型误设问题，本文提出将GP与流行的保形预测（CP）相结合——CP是一种无分布后处理框架，仅需数据可交换性假设即可生成具有可证明有效覆盖的预测集。然而，在线学习场景中，通常需要在真实标签揭示前获得预测集，这往往违背了可交换性假设。为确保长期覆盖保证，我们将根据真实标签是否落入预测集的反馈，自适应地调整关键阈值参数。数值实验结果表明，在线GP-CP方法在长期覆盖性能上优于现有替代方案。