🤖 AI Summary
This work proposes a novel approach that integrates normalizing flows with stratified sampling to estimate expectations without relying on restrictive (semi-)parametric distributional assumptions, such as Gaussian or Gaussian mixture models, which can introduce substantial bias when misspecified. By leveraging the expressive power of neural networks, the method flexibly captures complex, unknown data distributions, thereby overcoming the limitations of traditional parametric frameworks. Empirical evaluations demonstrate that the proposed estimator significantly reduces Monte Carlo uncertainty in high-dimensional settings—specifically in 30- and 128-dimensional problems—and achieves marked improvements in both accuracy and stability compared to conventional Monte Carlo estimators and Gaussian mixture model-based approaches.
📝 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.