# Gaussian Process Regression with Soft Inequality and Monotonicity Constraints

arXiv: https://arxiv.org/abs/2404.02873 · HTML: https://mlsanity.com/paper/2404.02873/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 3 Apr 2024.

## Builds on (most cited first, 11 of 11)

- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges](https://mlsanity.com/paper/2006.09319/) (2020)
- [Gaussian process emulators for computer experiments with inequality constraints](https://mlsanity.com/paper/1606.01265/) (2016)
- [Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence](https://mlsanity.com/paper/1811.09757/) (2018)
- [Gaussian processes with linear operator inequality constraints](https://mlsanity.com/paper/1901.03134/) (2019)
- [Linearly Constrained Gaussian Processes with Boundary Conditions](https://mlsanity.com/paper/2002.00818/) (2020)
- [Finite-dimensional Gaussian approximation with linear inequality constraints](https://mlsanity.com/paper/1710.07453/) (2017)
- [Nonnegativity-Enforced Gaussian Process Regression](https://mlsanity.com/paper/2004.04632/) (2020)
- [Quantum-Inspired Hamiltonian Monte Carlo for Bayesian Sampling](https://mlsanity.com/paper/1912.01937/) (2019)
- [High-dimensional additive Gaussian processes under monotonicity constraints](https://mlsanity.com/paper/2205.08528/) (2022)

## Abstract (arXiv)

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that enforces the physical constraints in a probabilistic manner. This GP model is trained by the quantum-inspired Hamiltonian Monte Carlo (QHMC). QHMC is an efficient way to sample from a broad class of distributions. Unlike the standard Hamiltonian Monte Carlo algorithm in which a particle has a fixed mass, QHMC allows a particle to have a random mass matrix with a probability distribution. Introducing the QHMC method to the inequality and monotonicity constrained GP regression in the probabilistic sense, our approach improves the accuracy and reduces the variance in the resulting GP model. According to our experiments on several datasets, the proposed approach serves as an efficient method as it accelerates the sampling process while maintaining the accuracy, and it is applicable to high dimensional problems.