Reducing Estimation Uncertainty Using Normalizing Flows and Stratification

• URL: http://arxiv.org/abs/2602.10706v3
• Date: Mon, 16 Feb 2026 21:31:37 GMT
• Title: Reducing Estimation Uncertainty Using Normalizing Flows and Stratification
• Authors: Paweł Lorek, Rafał Nowak, Rafał Topolnicki, Tomasz Trzciński, Maciej Zięba, Aleksandra Krystecka,
• Abstract summary: Current methodologies assume (semi-) distributions such as Gaussian or mixed Gaussian, leading to significant estimation uncertainty if these assumptions do not hold.<n>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.<n>Our model shows a marked reduction in estimation uncertainty across multiple datasets, including high-dimensional (30 and 128) ones.
• Score: 35.18016233072556
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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