# Bayesian Monotone Regression using Gaussian Process Projection

arXiv: https://arxiv.org/abs/1306.4041 · HTML: https://mlsanity.com/paper/1306.4041/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2013.

## Built on by (most cited first, 7 of 7)

- [Conditioning Gaussian Processes on Almost Anything](https://mlsanity.com/paper/2605.21041/) (2026)
- [Capturing and incorporating expert knowledge into machine learning models for quality prediction in manufacturing](https://mlsanity.com/paper/2202.02003/) (2022)
- [LatentFlow: A General Framework for Conditioning Stochastic Processes](https://mlsanity.com/paper/2607.12922/) (2026)
- [Aligned Multi-Task Gaussian Process](https://mlsanity.com/paper/2110.15761/) (2021)
- [Functional BART with Shape Priors: A Bayesian Tree Approach to Constrained Functional Regression](https://mlsanity.com/paper/2502.16888/) (2025)
- [Sequential Adaptive Priors for Orthogonal Functions](https://mlsanity.com/paper/2508.15552/) (2025)
- [Modeling nonstationary spatial processes with normalizing flows](https://mlsanity.com/paper/2509.12884/) (2025)

## Abstract (arXiv)

Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid implausible results. We propose two novel methods focusing on Bayesian monotone curve and surface estimation using Gaussian process projections. The first projects samples from an unconstrained prior, while the second projects samples from the Gaussian process posterior. Theory is developed on continuity of the projection, posterior consistency and rates of contraction. The second approach is shown to have an empirical Bayes justification and to lead to simple computation with good performance in finite samples. Our projection approach can be applied in other constrained function estimation problems including in multivariate settings.