[论文] Likelihood-free inference with nuisance parameters through normalizing flows (arXiv:2609.10534)

论文概要

研究领域: ML
作者: Phil Assheton
发布时间: 2026-09-09
arXiv: 2609.10534

中文摘要

本文提出一种简单的神经网络归一化流分解方法，能够在存在干扰参数(nuisance parameters)的情况下自然地揭示一个近似关键统计量(pivotal statistic)，且仅需来自目标分布的样本生成器。该统计量在最小平均KL散度意义下接近关键性，当统计量维度等于参数维度时具有良好的检验功效。它能够融入平移和尺度等群不变性的先验知识。该方法能几乎精确地发现单样本t检验，在约束方差比范围内的最坏情况尺寸上优于Welch检验，并在部分双列相关上实现良好的校准，同时在小到中等样本上比轮廓似然比技术具有更高的功效和更快的速度。

原文摘要

We present a simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic (or something close) in the presence of nuisance parameters, based only on a sample generator from the distribution of interest. We show that the statistic is near-pivotal in the sense of minimum average KL-divergence of its \(p\)-values versus uniform and we argue that it can be expected to have good power when the dimension of the statistic equals the dimension of the parameter. It is able to incorporate prior knowledge about group invariances such as translation and scale. It can discover the one-sample \(t\)-test almost exactly, outperforms the Welch test in terms of worst-case size over a constrained variance-ratio range and achieves good calibration on partial biserial correlations, while showing higher power (and being much faster) on small-to-moderate samples than profile likelihood-ratio techniques.

自动采集于 2026-09-11

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