# High-dimensional additive Gaussian processes under monotonicity constraints

arXiv: https://arxiv.org/abs/2205.08528 · HTML: https://mlsanity.com/paper/2205.08528/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 17 May 2022.

## Builds on (most cited first, 10 of 10)

- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Non-parametric Models for Non-negative Functions](https://mlsanity.com/paper/2007.03926/) (2020)
- [Randomly Projected Additive Gaussian Processes for Regression](https://mlsanity.com/paper/1912.12834/) (2019)
- [Gaussian process emulators for computer experiments with inequality constraints](https://mlsanity.com/paper/1606.01265/) (2016)
- [Finite-dimensional Gaussian approximation with linear inequality constraints](https://mlsanity.com/paper/1710.07453/) (2017)
- [Consistent Online Gaussian Process Regression Without the Sample Complexity Bottleneck](https://mlsanity.com/paper/2004.11094/) (2020)
- [Monotone Function Estimation for Computer Experiments](https://mlsanity.com/paper/1309.3802/) (2013)
- [Gaussian Process Modulated Cox Processes under Linear Inequality Constraints](https://mlsanity.com/paper/1902.10974/) (2019)
- [A Role for Symmetry in the Bayesian Solution of Differential Equations](https://mlsanity.com/paper/1906.10564/) (2019)
- [Approximating Gaussian Process Emulators with Linear Inequality Constraints and Noisy Observations via MC and MCMC](https://mlsanity.com/paper/1901.04827/) (2019)

## Built on by (most cited first, 4 of 4)

- [Bayesian Optimization with Preference Exploration using a Monotonic Neural Network Ensemble](https://mlsanity.com/paper/2501.18792/) (2025)
- [Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regression](https://mlsanity.com/paper/2403.13300/) (2024)
- [Gaussian Process Regression with Soft Inequality and Monotonicity Constraints](https://mlsanity.com/paper/2404.02873/) (2024)
- [Fast Gaussian Processes under Monotonicity Constraints](https://mlsanity.com/paper/2507.06677/) (2025)

## Abstract (arXiv)

We introduce an additive Gaussian process framework accounting for monotonicity constraints and scalable to high dimensions. Our contributions are threefold. First, we show that our framework enables to satisfy the constraints everywhere in the input space. We also show that more general componentwise linear inequality constraints can be handled similarly, such as componentwise convexity. Second, we propose the additive MaxMod algorithm for sequential dimension reduction. By sequentially maximizing a squared-norm criterion, MaxMod identifies the active input dimensions and refines the most important ones. This criterion can be computed explicitly at a linear cost. Finally, we provide open-source codes for our full framework. We demonstrate the performance and scalability of the methodology in several synthetic examples with hundreds of dimensions under monotonicity constraints as well as on a real-world flood application.