用流模型与分层采样降低统计估计不确定性
Reducing Estimation Uncertainty Using Normalizing Flows and Stratification
- 用神经网络构建可变分布模型，替代传统参数假设
- 在高维数据上显著降低估计误差，优于蒙特卡洛和混合高斯模型
- 适合需要高精度统计估计的研究者，如金融、物理模拟领域
从样本数据估计随机变量函数的期望是统计分析的核心任务，在诸多应用中具有深远影响。现有方法通常假设（半）参数分布（如高斯或混合高斯），若假设不成立则会导致显著估计不确定性。本文提出一种基于流的模型，结合分层采样，利用参数化神经网络实现对未知数据分布的更高灵活性建模，从而缓解该局限。实验显示，该模型在多个数据集（包括30维和128维高维数据）上均显著降低估计不确定性，优于原始蒙特卡洛估计器和高斯混合模型。代码已开源：https://github.com/rnoxy/flowstrat。
原文摘要 · Abstract (English)
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.
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