# Local Gaussian process approximation for large computer experiments

arXiv: https://arxiv.org/abs/1303.0383 · HTML: https://mlsanity.com/paper/1303.0383/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2013.

## Built on by (most cited first, 30 of 59)

- [Inducing Point Allocation for Sparse Gaussian Processes in High-Throughput Bayesian Optimisation](https://mlsanity.com/paper/2301.10123/) (2023)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks](https://mlsanity.com/paper/2105.04554/) (2021)
- [Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factors](https://mlsanity.com/paper/2106.15356/) (2021)
- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process Regression with Mat'ern Correlations](https://mlsanity.com/paper/2203.03116/) (2022)
- [Bayesian Calibration of Imperfect Computer Models using Physics-Informed Priors](https://mlsanity.com/paper/2201.06463/) (2022)
- [MuyGPs: Scalable Gaussian Process Hyperparameter Estimation Using Local Cross-Validation](https://mlsanity.com/paper/2104.14581/) (2021)
- [A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABC](https://mlsanity.com/paper/2108.00490/) (2021)
- [Non-smooth Bayesian Optimization in Tuning Problems](https://mlsanity.com/paper/2109.07563/) (2021)
- [Variational Nearest Neighbor Gaussian Process](https://mlsanity.com/paper/2202.01694/) (2022)
- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes](https://mlsanity.com/paper/2412.20375/) (2024)
- [Scalable Cross Validation Losses for Gaussian Process Models](https://mlsanity.com/paper/2105.11535/) (2021)
- [Traffic State Estimation from Vehicle Trajectories with Anisotropic Gaussian Processes](https://mlsanity.com/paper/2303.02311/) (2023)
- [Input Dependent Sparse Gaussian Processes](https://mlsanity.com/paper/2107.07281/) (2021)
- [Active Learning of Piecewise Gaussian Process Surrogates](https://mlsanity.com/paper/2301.08789/) (2023)
- [Voronoi Candidates for Bayesian Optimization](https://mlsanity.com/paper/2402.04922/) (2024)
- [Sensitivity Prewarping for Local Surrogate Modeling](https://mlsanity.com/paper/2101.06296/) (2021)
- [Learning particle swarming models from data with Gaussian processes](https://mlsanity.com/paper/2106.02735/) (2021)
- [All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogates](https://mlsanity.com/paper/2512.09060/) (2025)
- [High dimensional Bayesian Optimization Algorithm for Complex System in Time Series](https://mlsanity.com/paper/2108.02289/) (2021)
- [Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functions](https://mlsanity.com/paper/2210.09168/) (2022)
- [Trajectory-oriented optimization of stochastic epidemiological models](https://mlsanity.com/paper/2305.03926/) (2023)
- [A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling](https://mlsanity.com/paper/2305.10158/) (2023)
- [Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box Simulators with Noise Parameters](https://mlsanity.com/paper/2403.03816/) (2024)
- [Posterior Covariance Structures in Gaussian Processes](https://mlsanity.com/paper/2408.07379/) (2024)
- [Modular Jump Gaussian Processes](https://mlsanity.com/paper/2505.15557/) (2025)
- [Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functions](https://mlsanity.com/paper/2510.21974/) (2025)
- [Fast Gaussian Process Approximations for Autocorrelated Data](https://mlsanity.com/paper/2512.02925/) (2025)

## Abstract (arXiv)

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the support of a Gaussian process predictor based on a local subset of the data. We further derive expressions for fast sequential updating of all needed quantities as the local designs are built-up iteratively. Then we show how independent application of our local design strategy across the elements of a vast predictive grid facilitates a trivially parallel implementation. The end result is a global predictor able to take advantage of modern multicore architectures, while at the same time allowing for a nonstationary modeling feature as a bonus. We demonstrate our method on two examples utilizing designs sized in the thousands, and tens of thousands of data points. Comparisons are made to the method of compactly supported covariances.