# Additive Gaussian Process Regression

arXiv: https://arxiv.org/abs/1411.7009 · HTML: https://mlsanity.com/paper/1411.7009/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2014.

## Built on by (most cited first, 3 of 3)

- [Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?](https://mlsanity.com/paper/2301.12844/) (2023)
- [Fast and Scalable Spike and Slab Variable Selection in High-Dimensional Gaussian Processes](https://mlsanity.com/paper/2111.04558/) (2021)
- [Categorical Optimization with Bayesian Anchored Latent Trust Regions for Structural Design under High-Dimensional Uncertainty](https://mlsanity.com/paper/2604.25241/) (2026)

## Abstract (arXiv)

Additive-interactive regression has recently been shown to offer attractive minimax error rates over traditional nonparametric multivariate regression in a wide variety of settings, including cases where the predictor count is much larger than the sample size and many of the predictors have important effects on the response, potentially through complex interactions. We present a Bayesian implementation of additive-interactive regression using an additive Gaussian process (AGP) prior and develop an efficient Markov chain sampler that extends stochastic search variable selection in this setting. Careful prior and hyper-parameter specification are developed in light of performance and computational considerations, and key innovations address difficulties in exploring a joint posterior distribution over multiple subsets of high dimensional predictor inclusion vectors. The method offers state-of-the-art support and interaction recovery while improving dramatically over competitors in terms of prediction accuracy on a diverse set of simulated and real data. Results from real data studies provide strong evidence that the additive-interactive framework is an attractive modeling platform for high-dimensional nonparametric regression.