# Gaussian Process Regression and Classification under Mathematical Constraints with Learning Guarantees

arXiv: https://arxiv.org/abs/1904.09632 · HTML: https://mlsanity.com/paper/1904.09632/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2019.

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

- [Towards a Unified Framework for Uncertainty-aware Nonlinear Variable Selection with Theoretical Guarantees](https://mlsanity.com/paper/2204.07293/) (2022)

## Abstract (arXiv)

We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with closed-form probability density function (PDF), and has the attractive feature that its posterior distributions for regression and classification are again CGPs with closed-form expressions. Furthermore, we show that CGP inherents the optimal theoretical properties of the Gaussian process, e.g. rates of posterior contraction, due to the fact that CGP is an Gaussian process with a more efficient model space.