# Gaussian Process Regression for Maximum Entropy Distribution

arXiv: https://arxiv.org/abs/2308.06149 · HTML: https://mlsanity.com/paper/2308.06149/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 39 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Builds on (most cited first, 2 of 2)

- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Kernel Flows: from learning kernels from data into the abyss](https://mlsanity.com/paper/1808.04475/) (2018)

## Abstract (arXiv)

Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck for practical closure settings. Motivated by recent success of Gaussian processes, we investigate the suitability of Gaussian priors to approximate the Lagrange multipliers as a map of a given set of moments. Examining various kernel functions, the hyperparameters are optimized by maximizing the log-likelihood. The performance of the devised data-driven Maximum-Entropy closure is studied for couple of test cases including relaxation of non-equilibrium distributions governed by Bhatnagar-Gross-Krook and Boltzmann kinetic equations.