# Density estimation on small datasets

arXiv: https://arxiv.org/abs/1804.01932 · HTML: https://mlsanity.com/paper/1804.01932/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2018.

## Built on by (most cited first, 2 of 2)

- [Causal, Bayesian, & Non-parametric Modeling of the SARS-CoV-2 Viral Load Distribution vs. Patient's Age](https://mlsanity.com/paper/2105.13483/) (2021)
- [Learning to Wait: Synchronizing Agents with the Physical World](https://mlsanity.com/paper/2512.16262/) (2025)

## Abstract (arXiv)

How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one dimension, providing an exact nonparametric Bayesian posterior without relying on tunable parameters or large-data approximations. Strong non-Gaussian constraints, which require a non-perturbative treatment, are found to play a major role in reducing distribution uncertainty. A software implementation of this method is provided.