# Monotonic Gaussian Process Flow

arXiv: https://arxiv.org/abs/1905.12930 · HTML: https://mlsanity.com/paper/1905.12930/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 5 of 5)

- [Variational multiple shooting for Bayesian ODEs with Gaussian processes](https://mlsanity.com/paper/2106.10905/) (2021)
- [Monotonic Gaussian process for physics-constrained machine learning with materials science applications](https://mlsanity.com/paper/2209.00628/) (2022)
- [Conditional Deep Gaussian Processes: empirical Bayes hyperdata learning](https://mlsanity.com/paper/2110.00568/) (2021)
- [Aligned Multi-Task Gaussian Process](https://mlsanity.com/paper/2110.15761/) (2021)
- [Ice Core Dating using Probabilistic Programming](https://mlsanity.com/paper/2210.16568/) (2022)

## Abstract (arXiv)

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty. We demonstrate the efficacy of the proposed model by providing competitive results to other probabilistic monotonic models on a number of benchmark functions. In addition, we consider the utility of a monotonic random process as a part of a hierarchical probabilistic model; we examine the task of temporal alignment of time-series data where it is beneficial to use a monotonic random process in order to preserve the uncertainty in the temporal warpings.