Reducing Estimation Uncertainty Using Normalizing Flows and Stratification
Abstract
Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume (semi-)parametric distributions such as Gaussian or mixed Gaussian, leading to significant estimation uncertainty if these assumptions do not hold. We propose a flow-based model, integrated with stratified sampling, that leverages a parametrized neural network to offer greater flexibility in modeling unknown data distributions, thereby mitigating this limitation. Our model shows a marked reduction in estimation uncertainty across multiple datasets, including high-dimensional (30 and 128) ones, outperforming crude Monte Carlo estimators and Gaussian mixture models. Reproducible code is available at https://github.com/rnoxy/flowstrat.
Cite
@article{arxiv.2602.10706,
title = {Reducing Estimation Uncertainty Using Normalizing Flows and Stratification},
author = {Paweł Lorek and Rafał Nowak and Rafał Topolnicki and Tomasz Trzciński and Maciej Zięba and Aleksandra Krystecka},
journal= {arXiv preprint arXiv:2602.10706},
year = {2026}
}
Comments
This is the extended version of a paper accepted for publication at ACIIDS 2026