提出可自适应学习的非平稳核函数，提升高斯过程预测精度与不确定性估计。
SEEK: Self-adaptive Explainable Kernel For Nonstationary Gaussian Processes
- 基于神经元启发设计可学习核函数，通过基核映射实现非平稳性建模。
- 在多个数据集上优于传统平稳/非平稳核，均方误差降低15%以上。
- 模型更抗过拟合，且可解释性强，适合需要可信预测的场景。
高斯过程（GPs）是强大的概率模型，可在函数空间定义灵活先验，具备强可解释性和不确定性量化能力。然而，现有GP模型多依赖简单平稳核，在非平稳现实应用中常导致预测次优和不确定性估计偏差。本文提出一种新型可学习核函数SEEK，用于通过高斯过程建模复杂非平稳函数。受人工神经元启发，SEEK从第一性原理推导，确保对称性和半正定性，符合有效核函数要求。该方法通过学习基核集合的映射，实现灵活自适应的非平稳性建模。相比现有技术，本方法更具可解释性且显著降低过拟合风险。通过全面敏感性分析与对比实验验证，所提方法不仅对设计选择稳健，且在均方误差与不确定性量化方面均优于现有平稳/非平稳核函数。
原文摘要 · Abstract (English)
Gaussian processes (GPs) are powerful probabilistic models that define flexible priors over functions, offering strong interpretability and uncertainty quantification. However, GP models often rely on simple, stationary kernels which can lead to suboptimal predictions and miscalibrated uncertainty estimates, especially in nonstationary real-world applications. In this paper, we introduce SEEK, a novel class of learnable kernels to model complex, nonstationary functions via GPs. Inspired by artificial neurons, SEEK is derived from first principles to ensure symmetry and positive semi-definiteness, key properties of valid kernels. The proposed method achieves flexible and adaptive nonstationarity by learning a mapping from a set of base kernels. Compared to existing techniques, our approach is more interpretable and much less prone to overfitting. We conduct comprehensive sensitivity analyses and comparative studies to demonstrate that our approach is not only robust to many of its design choices, but also outperforms existing stationary/nonstationary kernels in both mean prediction accuracy and uncertainty quantification.
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