# Deep Random Features for Scalable Interpolation of Spatiotemporal Data

arXiv: https://arxiv.org/abs/2412.11350 · HTML: https://mlsanity.com/paper/2412.11350/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 48 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 3 of 3)

- [The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphs](https://mlsanity.com/paper/2407.08086/) (2024)
- [Robust Gaussian Process Regression with Huber Likelihood](https://mlsanity.com/paper/2301.07858/) (2023)
- [On Connecting Deep Trigonometric Networks with Deep Gaussian Processes: Covariance, Expressivity, and Neural Tangent Kernel](https://mlsanity.com/paper/2203.07411/) (2022)

## Built on by (most cited first, 6 of 6)

- [Measuring the Intrinsic Dimension of Earth Representations](https://mlsanity.com/paper/2511.02101/) (2025)
- [FloeNet: A mass-conserving global sea ice emulator that generalizes across climates](https://mlsanity.com/paper/2603.12449/) (2026)
- [Localized, High-resolution Geographic Representations with Slepian Functions](https://mlsanity.com/paper/2602.00392/) (2026)
- [Scalable Random Wavelet Features: Efficient Non-Stationary Kernel Approximation with Convergence Guarantees](https://mlsanity.com/paper/2602.00987/) (2026)
- [STACI: Spatio-Temporal Aleatoric Conformal Inference](https://mlsanity.com/paper/2505.21658/) (2025)
- [KunPeng: A Global Ocean Environmental Model](https://mlsanity.com/paper/2504.04766/) (2025)

## Abstract (arXiv)

The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes (GPs) are candidate model choices for interpolation. However, due to their poor scalability, they usually rely on inducing points for inference, which restricts their expressivity. Moreover, commonly imposed assumptions such as stationarity prevents them from capturing complex patterns in the data. While deep GPs can overcome this issue, training and making inference with them are difficult, again requiring crude approximations via inducing points. In this work, we instead approach the problem through Bayesian deep learning, where spatiotemporal fields are represented by deep neural networks, whose layers share the inductive bias of stationary GPs on the plane/sphere via random feature expansions. This allows one to (1) capture high frequency patterns in the data, and (2) use mini-batched gradient descent for large scale training. We experiment on various remote sensing data at local/global scales, showing that our approach produce competitive or superior results to existing methods, with well-calibrated uncertainties.