# Fast prediction of deterministic functions using sparse grid experimental designs

arXiv: https://arxiv.org/abs/1402.6350 · HTML: https://mlsanity.com/paper/1402.6350/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2014.

## Built on by (most cited first, 7 of 7)

- [Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process Regression with Mat'ern Correlations](https://mlsanity.com/paper/2203.03116/) (2022)
- [A Sparse Expansion For Deep Gaussian Processes](https://mlsanity.com/paper/2112.05888/) (2021)
- [Kernel Interpolation with Sparse Grids](https://mlsanity.com/paper/2305.14451/) (2023)
- [High-Dimensional Simulation Optimization via Brownian Fields and Sparse Grids](https://mlsanity.com/paper/2107.08595/) (2021)
- [Privacy-aware Gaussian Process Regression](https://mlsanity.com/paper/2305.16541/) (2023)
- [Beyond State Space Representation: A General Theory for Kernel Packets](https://mlsanity.com/paper/2402.04022/) (2024)
- [Gaussian Processes Sampling with Sparse Grids under Additive Schwarz Preconditioner](https://mlsanity.com/paper/2408.00206/) (2024)

## Abstract (arXiv)

Random field models have been widely employed to develop a predictor of an expensive function based on observations from an experiment. The traditional framework for developing a predictor with random field models can fail due to the computational burden it requires. This problem is often seen in cases where the input of the expensive function is high dimensional. While many previous works have focused on developing an approximative predictor to resolve these issues, this article investigates a different solution mechanism. We demonstrate that when a general set of designs is employed, the resulting predictor is quick to compute and has reasonable accuracy. The fast computation of the predictor is made possible through an algorithm proposed by this work. This paper also demonstrates methods to quickly evaluate the likelihood of the observations and describes some fast maximum likelihood estimates for unknown parameters of the random field. The computational savings can be several orders of magnitude when the input is located in a high dimensional space. Beyond the fast computation of the predictor, existing research has demonstrated that a subset of these designs generate predictors that are asymptotically efficient. This work details some empirical comparisons to the more common space-filling designs that verify the designs are competitive in terms of resulting prediction accuracy.