# Combining additivity and active subspaces for high-dimensional Gaussian process modeling

arXiv: https://arxiv.org/abs/2402.03809 · HTML: https://mlsanity.com/paper/2402.03809/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 64 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Multi-Information Source Optimization](https://mlsanity.com/paper/1603.00389/) (2016)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Active Learning of Linear Embeddings for Gaussian Processes](https://mlsanity.com/paper/1310.6740/) (2013)
- [Inducing Point Allocation for Sparse Gaussian Processes in High-Throughput Bayesian Optimisation](https://mlsanity.com/paper/2301.10123/) (2023)
- [Transfer Learning with Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2111.11223/) (2021)
- [Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities](https://mlsanity.com/paper/2006.16728/) (2020)
- [Randomly Projected Additive Gaussian Processes for Regression](https://mlsanity.com/paper/1912.12834/) (2019)
- [Additive Gaussian Processes Revisited](https://mlsanity.com/paper/2206.09861/) (2022)
- [Sequential Learning of Active Subspaces](https://mlsanity.com/paper/1907.11572/) (2019)
- [High Dimensional Bayesian Optimization Assisted by Principal Component Analysis](https://mlsanity.com/paper/2007.00925/) (2020)
- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality](https://mlsanity.com/paper/2003.09673/) (2020)
- [Constrained global optimization of functions with low effective dimensionality using multiple random embeddings](https://mlsanity.com/paper/2009.10446/) (2020)
- [Sensitivity Prewarping for Local Surrogate Modeling](https://mlsanity.com/paper/2101.06296/) (2021)

## Built on by (most cited first, 1 of 1)

- [Uncertainty-Aware Out-of-Distribution Detection with Gaussian Processes](https://mlsanity.com/paper/2412.20918/) (2024)

## Abstract (arXiv)

Gaussian processes are a widely embraced technique for regression due to their good prediction accuracy, analytical tractability, and built-in capabilities for uncertainty quantification. However, they suffer from the curse of dimensionality whenever the number of variables increases. This challenge is generally addressed by assuming additional structure in the problem, the preferred options being either additivity or low intrinsic dimensionality. After discussing their relative merits, our contribution for high-dimensional Gaussian process modeling is to combine them with a multi-fidelity strategy. We detail the corresponding construction and showcase the advantages through experiments on synthetic functions and datasets.