# Finite-dimensional Gaussian approximation with linear inequality constraints

arXiv: https://arxiv.org/abs/1710.07453 · HTML: https://mlsanity.com/paper/1710.07453/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2017.

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- [Beyond Surrogate Modeling: Learning the Local Volatility Via Shape Constraints](https://mlsanity.com/paper/2212.09957/) (2022)
- [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)
- [Constrained Probabilistic Numerics: Gaussian Process Solvers for Linear PDEs under Linear Inequality Constraints](https://mlsanity.com/paper/2610.13804/) (2026)

## Abstract (arXiv)

Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017) which can satisfy inequality conditions everywhere (either boundedness, monotonicity or convexity). Our contributions are threefold. First, we extend their approach in order to deal with general sets of linear inequalities. Second, we explore several Markov Chain Monte Carlo (MCMC) techniques to approximate the posterior distribution. Third, we investigate theoretical and numerical properties of the constrained likelihood for covariance parameter estimation. According to experiments on both artificial and real data, our full framework together with a Hamiltonian Monte Carlo-based sampler provides efficient results on both data fitting and uncertainty quantification.