提出新方法处理带负权重的粒子物理数据分析问题
Neural Quasiprobabilistic Likelihood Ratio Estimation with Negatively Weighted Data
- 用带符号混合模型分解似然比，支持负概率密度
- 设计新损失函数应对负权重带来的训练挑战
- 在真实粒子物理数据上验证方法有效性
针对高能粒子物理中的实际场景，本文将似然比估计推广到允许概率密度为负的准概率设置。在此框架下，重要性采样也可包含负权重。传统神经似然比估计方法难以应对负密度和负权重带来的挑战。为此，本文提出一种新型损失函数，并设计基于符号混合模型分解的新型网络架构，作为第二条解决路径。实验部分在教学示例和真实的粒子物理案例上验证了该方法的有效性。
原文摘要 · Abstract (English)
Motivated by real-world situations found in high energy particle physics, we consider a generalisation of the likelihood-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. By extension, this framing also applies to importance sampling in a setting where the importance weights can be negative. The presence of negative densities and negative weights, pose an array of challenges to traditional neural likelihood ratio estimation methods. We address these challenges by introducing a novel loss function. In addition, we introduce a new model architecture based on the decomposition of a likelihood ratio using signed mixture models, providing a second strategy for overcoming these challenges. Finally, we demonstrate our approach on a pedagogical example and a real-world example from particle physics.
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