# Approximating Gaussian Process Emulators with Linear Inequality Constraints and Noisy Observations via MC and MCMC

arXiv: https://arxiv.org/abs/1901.04827 · HTML: https://mlsanity.com/paper/1901.04827/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2019.

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

- [High-dimensional additive Gaussian processes under monotonicity constraints](https://mlsanity.com/paper/2205.08528/) (2022)

## Abstract (arXiv)

Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov Chain Monte Carlo (MCMC) methods. However, strictly interpolating the observations may entail expensive computations due to highly restrictive sample spaces. Furthermore, having (constrained) GP emulators when data are actually noisy is also of interest for real-world implementations. Hence, we introduce a noise term for the relaxation of the interpolation conditions, and we develop the corresponding approximation of GP emulators under linear inequality constraints. We show with various toy examples that the performance of MC and MCMC samplers improves when considering noisy observations. Finally, on 2D and 5D coastal flooding applications, we show that more flexible and realistic GP implementations can be obtained by considering noise effects and by enforcing the (linear) inequality constraints.