Reducing Estimation Uncertainty Using Normalizing Flows and Stratification
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908837193187328 |
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| author | Lorek, Paweł Nowak, Rafał Topolnicki, Rafał Trzciński, Tomasz Zięba, Maciej Krystecka, Aleksandra |
| author_facet | Lorek, Paweł Nowak, Rafał Topolnicki, Rafał Trzciński, Tomasz Zięba, Maciej Krystecka, Aleksandra |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10706 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reducing Estimation Uncertainty Using Normalizing Flows and Stratification Lorek, Paweł Nowak, Rafał Topolnicki, Rafał Trzciński, Tomasz Zięba, Maciej Krystecka, Aleksandra Machine Learning 65C05 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. |
| title | Reducing Estimation Uncertainty Using Normalizing Flows and Stratification |
| topic | Machine Learning 65C05 |
| url | https://arxiv.org/abs/2602.10706 |