发表机构
Department of Physics, University of Massachusetts Amherst; Data Science Institute, University of Wisconsin–Madison（马萨诸塞大学阿默斯特分校物理系; 威斯康星大学麦迪逊分校数据科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出混合神经密度估计方法，结合流模型与分类器，实现可评估密度替代与精确Asimov数据集构造，用于高维无分箱仿真推断。
AI 中文摘要
高维、无分箱的神经仿真推断通常依赖于神经比率估计，该方法使用表达力强的监督模型来估计密度比，但学习到的比率本身既不提供显式的归一化密度，也不提供生成模型。基于流的替代模型则能够实现可处理的密度评估和高效采样，但残余的密度估计误差可能限制复杂隐式分布的精度。我们提出混合神经密度估计，该方法使用一个流来定义与参数无关的参考分布，并使用分类器来估计目标与参考之间的密度比。将学习到的比率乘以参考密度，即可得到可评估的目标密度替代。该比率还提供了用于积分和重采样的重要性权重。我们展示了这种表示如何构造一个精确的Asimov数据集，其最大似然拟合可返回生成参数。我们还展示了可处理的参考分布如何为伪实验提供可再生样本，以及如何利用它来降低期望检验统计量计算的蒙特卡洛方差。我们在一个受高能物理测量启发的玩具统计模型中演示了该构造，该模型的精确密度是解析已知的。
英文摘要
High-dimensional, unbinned neural simulation-based inference often relies on neural ratio estimation, which uses expressive supervised models to estimate density ratios, but a learned ratio by itself provides neither an explicit normalized density nor a generative model. Flow-based surrogate models instead enable tractable density evaluation and efficient sampling, but residual density-estimation errors can limit precision for complex implicit distributions. We propose \textit{hybrid neural density estimation}, which uses a flow to define a parameter-independent reference distribution, and classifiers to estimate target-to-reference density ratios. Multiplying a learned ratio by the reference density gives an evaluable target density surrogate. The ratio also provides importance weights for integration and resampling. We show how this representation defines an exact Asimov dataset, whose maximum likelihood fit returns the generating parameters. We also show how the tractable reference supplies renewable samples for pseudo-experiments and how it enables methods to reduce the Monte Carlo variance of expected test statistic calculations. We demonstrate the construction in a toy statistical model motivated by high-energy physics measurements, but for which the exact densities are known analytically.
Comments35 pages, 10 figures
