# SEEK: Self-adaptive Explainable Kernel For Nonstationary Gaussian Processes

arXiv: https://arxiv.org/abs/2503.14785 · HTML: https://mlsanity.com/paper/2503.14785/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1508.04319/) (2015)
- [GP+: A Python Library for Kernel-based learning via Gaussian Processes](https://mlsanity.com/paper/2312.07694/) (2023)
- [Deep Structured Mixtures of Gaussian Processes](https://mlsanity.com/paper/1910.04536/) (2019)
- [Improving Output Uncertainty Estimation and Generalization in Deep Learning via Neural Network Gaussian Processes](https://mlsanity.com/paper/1707.05922/) (2017)
- [Exact Gaussian Processes for Massive Datasets via Non-Stationary Sparsity-Discovering Kernels](https://mlsanity.com/paper/2205.09070/) (2022)
- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Neural Non-Stationary Spectral Kernel](https://mlsanity.com/paper/1811.10978/) (2018)
- [Dynamic Online Ensembles of Basis Expansions](https://mlsanity.com/paper/2405.01365/) (2024)
- [Synthetic data generation method for data-free knowledge distillation in regression neural networks](https://mlsanity.com/paper/2301.04338/) (2023)
- [KTBoost: Combined Kernel and Tree Boosting](https://mlsanity.com/paper/1902.03999/) (2019)
- [Sparse Spectrum Warped Input Measures for Nonstationary Kernel Learning](https://mlsanity.com/paper/2010.04315/) (2020)
- [Adaptive Robotic Information Gathering via Non-Stationary Gaussian Processes](https://mlsanity.com/paper/2306.01263/) (2023)

## Abstract (arXiv)

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.