Reducing Estimation Uncertainty Using Normalizing Flows and Stratification
This work addresses estimation uncertainty in statistical applications, offering a more flexible approach for modeling unknown data distributions, but it appears incremental as it builds on existing flow-based and stratified sampling techniques.
The paper tackled the problem of reducing estimation uncertainty in statistical analysis by proposing a flow-based model integrated with stratified sampling, which outperformed existing methods like crude Monte Carlo and Gaussian mixture models, showing marked reductions in uncertainty across datasets including high-dimensional ones (30 and 128 dimensions).
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.