分析了组合评分算法在模拟推断中的误差累积问题
Error analysis of a compositional score-based algorithm for simulation-based inference
- 通过理论推导给出组合评分的均方误差上界
- 发现观测数量增加会放大个体评分误差
- 适用于需要高精度参数推断的研究者
模拟推断（SBI）已成为应用科学中估计随机模型参数以解释实验观测的常用框架。核心问题是如何有效结合多个观测以提升参数推断并获得更尖锐的后验分布。最近的基于得分的扩散方法通过在扩散过程中聚合单个后验得分来构建组合得分，解决了这一问题。尽管人们自然推测，随着观测数量增加，个体误差的累积可能显著降低采样质量，但这一关键理论问题至今未被探索。本文研究了Linhart等人（2024）提出的GAUSS算法生成的组合得分，并建立了其均方误差的上界，该上界同时依赖于个体得分误差和观测数量。我们通过一个高斯示例验证了理论结果，其中所有解析表达式均可闭合形式求解。
原文摘要 · Abstract (English)
Simulation-based inference (SBI) has become a widely used framework in applied sciences for estimating the parameters of stochastic models that best explain experimental observations. A central question in this setting is how to effectively combine multiple observations in order to improve parameter inference and obtain sharper posterior distributions. Recent advances in score-based diffusion methods address this problem by constructing a compositional score, obtained by aggregating individual posterior scores within the diffusion process. While it is natural to suspect that the accumulation of individual errors may significantly degrade sampling quality as the number of observations grows, this important theoretical issue has so far remained unexplored. In this paper, we study the compositional score produced by the GAUSS algorithm of Linhart et al. (2024) and establish an upper bound on its mean squared error in terms of both the individual score errors and the number of observations. We illustrate our theoretical findings on a Gaussian example, where all analytical expressions can be derived in a closed form.
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