# Scalable Gaussian Processes with Latent Kronecker Structure

arXiv: https://arxiv.org/abs/2506.06895 · HTML: https://mlsanity.com/paper/2506.06895/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 7 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Auto-PyTorch Tabular: Multi-Fidelity MetaLearning for Efficient and Robust AutoDL](https://mlsanity.com/paper/2006.13799/) (2020)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [Scalable Log Determinants for Gaussian Process Kernel Learning](https://mlsanity.com/paper/1711.03481/) (2017)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Product Kernel Interpolation for Scalable Gaussian Processes](https://mlsanity.com/paper/1802.08903/) (2018)
- [Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent](https://mlsanity.com/paper/2306.11589/) (2023)
- [Bayesian Active Learning with Fully Bayesian Gaussian Processes](https://mlsanity.com/paper/2205.10186/) (2022)
- [Stochastic Gradient Descent for Gaussian Processes Done Right](https://mlsanity.com/paper/2310.20581/) (2023)
- [Computation-Aware Kalman Filtering and Smoothing](https://mlsanity.com/paper/2405.08971/) (2024)
- [Large-Scale Gaussian Processes via Alternating Projection](https://mlsanity.com/paper/2310.17137/) (2023)
- [Scalable First-Order Bayesian Optimization via Structured Automatic Differentiation](https://mlsanity.com/paper/2206.08366/) (2022)
- [SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes](https://mlsanity.com/paper/2106.06695/) (2021)
- [Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference](https://mlsanity.com/paper/2411.01036/) (2024)
- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [The Fast Kernel Transform](https://mlsanity.com/paper/2106.04487/) (2021)
- [Improving Linear System Solvers for Hyperparameter Optimisation in Iterative Gaussian Processes](https://mlsanity.com/paper/2405.18457/) (2024)

## Built on by (most cited first, 5 of 5)

- [Graph Random Features for Scalable Gaussian Processes](https://mlsanity.com/paper/2509.03691/) (2025)
- [Successive Halving with Learning Curve Prediction via Latent Kronecker Gaussian Processes](https://mlsanity.com/paper/2508.14818/) (2025)
- [Empirical Gaussian Processes](https://mlsanity.com/paper/2602.12082/) (2026)
- [Scalable Gaussian process inference via neural feature maps](https://mlsanity.com/paper/2605.10285/) (2026)
- [Target-Constrained Pooling for Trajectory Extrapolation](https://mlsanity.com/paper/2610.13034/) (2026)

## Abstract (arXiv)

Applying Gaussian processes (GPs) to very large datasets remains a challenge due to limited computational scalability. Matrix structures, such as the Kronecker product, can accelerate operations significantly, but their application commonly entails approximations or unrealistic assumptions. In particular, the most common path to creating a Kronecker-structured kernel matrix is by evaluating a product kernel on gridded inputs that can be expressed as a Cartesian product. However, this structure is lost if any observation is missing, breaking the Cartesian product structure, which frequently occurs in real-world data such as time series. To address this limitation, we propose leveraging latent Kronecker structure, by expressing the kernel matrix of observed values as the projection of a latent Kronecker product. In combination with iterative linear system solvers and pathwise conditioning, our method facilitates inference of exact GPs while requiring substantially fewer computational resources than standard iterative methods. We demonstrate that our method outperforms state-of-the-art sparse and variational GPs on real-world datasets with up to five million examples, including robotics, automated machine learning, and climate applications.