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.

翻译：从样本数据中估计随机变量实值函数的期望是统计分析的关键环节，在各类应用中具有深远影响。现有方法通常假设（半）参数化分布（如高斯分布或混合高斯分布），若这些假设不成立则会导致显著的估计不确定性。我们提出一种结合分层抽样的流式模型，该模型利用参数化神经网络为未知数据分布建模提供更强的灵活性，从而缓解这一局限。我们的模型在多个数据集（包括高维（30维与128维）数据集）上均显示出估计不确定性的显著降低，其性能优于原始蒙特卡洛估计器与高斯混合模型。可复现代码详见 https://github.com/rnoxy/flowstrat。