Non-Stationary Kernel Learning in Gaussian Processes

Abstract 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 article, we introduce self-adaptive explainable kernel (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.