Reducing Estimation Uncertainty Using Normalizing Flows and Stratification

TL;DR

This paper introduces a flow-based model combined with stratified sampling to reduce estimation uncertainty in statistical expectation calculations, especially when data distributions are unknown or complex.

Contribution

It presents a novel integration of normalizing flows with stratification, improving estimation accuracy over traditional methods in high-dimensional settings.

Findings

Significant reduction in estimation uncertainty across multiple datasets.

Outperforms Gaussian mixture models and Monte Carlo estimators.

Effective in high-dimensional data (30 and 128 dimensions).

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.