提出一种紧致的核回归不确定度边界，可处理相关噪声。
Optimal kernel regression bounds under energy-bounded noise
- 基于函数与噪声的范数有界假设，构造最坏情况下的估计边界。
- 边界计算仅需解一个优化问题，且在最优噪声协方差下等价于GP后验均值与协方差。
- 适用于安全关键场景中的模型可信度评估，尤其适合核方法使用者。
非保守的不确定性边界对于评估估计算法的准确性及下游应用（如安全关键系统部署）至关重要。本文推导了核估计的一种紧致、非渐近的不确定性边界，可处理相关噪声序列。该边界依赖于对未知函数和噪声的温和范数有界假设，能够返回在任意查询点处假设类中可能的最坏函数实现。该函数值被证明在测量噪声协方差取最优时，等价于高斯过程的后验均值与协方差。通过严格分析与文献结果对比，验证了该方法在生成紧致且易计算的核估计不确定性边界方面的有效性。
原文摘要 · Abstract (English)
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic uncertainty bound for kernel-based estimation, which can also handle correlated noise sequences. Its computation relies on a mild norm-boundedness assumption on the unknown function and the noise, returning the worst-case function realization within the hypothesis class at an arbitrary query input location. The value of this function is shown to be given in terms of the posterior mean and covariance of a Gaussian process for an optimal choice of the measurement noise covariance. By rigorously analyzing the proposed approach and comparing it with other results in the literature, we show its effectiveness in returning tight and easy-to-compute bounds for kernel-based estimates.
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