用机器学习加速高能物理全局拟合，高效探索新粒子参数空间。
Lecture notes on Machine Learning applications for global fits
- 用提升决策树逼近对数似然函数，降低计算成本。
- 结合主动学习与高斯过程生成数据，实现高效训练。
- 可解释性分析揭示参数间相互作用，适合新物理研究者。
这些讲义提供了一个完整的框架，用于在高能物理中使用现代机器学习代理进行全局统计拟合。首先回顾了模型构建的统计基础，包括似然函数、威尔克斯定理和轮廓似然。考虑到模型预测的计算开销常使传统最小化方法不可行，引入提升决策树来近似对数似然函数。讲义详细介绍了稳健的机器学习流程：通过主动学习与高斯过程高效生成训练数据，进行超参数优化，模型编译以提升速度，并利用SHAP值实现可解释性，解析模型参数及其相互作用的影响。进一步讨论了使用马尔可夫链蒙特卡洛（MCMC）进行后验分布采样。最后，该方法应用于B±→K±νν̄异常问题，展示两阶段机器学习模型如何高效探索轴子类粒子（ALPs）的参数空间，同时满足衰变长度和味破坏耦合的严格实验约束。
原文摘要 · Abstract (English)
These lecture notes provide a comprehensive framework for performing global statistical fits in high-energy physics using modern Machine Learning (ML) surrogates. We begin by reviewing the statistical foundations of model building, including the likelihood function, Wilks' theorem, and profile likelihoods. Recognizing that the computational cost of evaluating model predictions often renders traditional minimization prohibitive, we introduce Boosted Decision Trees to approximate the log-likelihood function. The notes detail a robust ML workflow including efficient generation of training data with active learning and Gaussian processes, hyperparameter optimization, model compilation for speed-up, and interpretability through SHAP values to decode the influence of model parameters and interactions between parameters. We further discuss posterior distribution sampling using Markov Chain Monte Carlo (MCMC). These techniques are finally applied to the $B^\pm \to K^\pm ν\barν$ anomaly at Belle II, demonstrating how a two-stage ML model can efficiently explore the parameter space of Axion-Like Particles (ALPs) while satisfying stringent experimental constraints on decay lengths and flavor-violating couplings.
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