# Sparse Spectrum Warped Input Measures for Nonstationary Kernel Learning

arXiv: https://arxiv.org/abs/2010.04315 · HTML: https://mlsanity.com/paper/2010.04315/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [Uncertainty Disentanglement with Non-stationary Heteroscedastic Gaussian Processes for Active Learning](https://mlsanity.com/paper/2210.10964/) (2022)
- [Scalable Random Wavelet Features: Efficient Non-Stationary Kernel Approximation with Convergence Guarantees](https://mlsanity.com/paper/2602.00987/) (2026)
- [SEEK: Self-adaptive Explainable Kernel For Nonstationary Gaussian Processes](https://mlsanity.com/paper/2503.14785/) (2025)

## Abstract (arXiv)

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness with respect to the input. The proposed learning algorithm warps inputs as conditional Gaussian measures that control the smoothness of a standard stationary kernel. This construction allows us to capture non-stationary patterns in the data and provides intuitive inductive bias. The resulting method is based on sparse spectrum Gaussian processes, enabling closed-form solutions, and is extensible to a stacked construction to capture more complex patterns. The method is extensively validated alongside related algorithms on synthetic and real world datasets. We demonstrate a remarkable efficiency in the number of parameters of the warping functions in learning problems with both small and large data regimes.