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arXiv · 1804.01932

Density estimation on small datasets

Wei-Chia Chen·Ammar Tareen·Justin B. Kinney
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Abstract

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.

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BibTeXRIS

Wei-Chia Chen, Ammar Tareen, Justin B. Kinney. 2018-04-05. Density estimation on small datasets. https://doi.org/10.1103/physrevlett.121.160605

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