Global fits in high energy physics and cosmology often face the challenge of exploring high-dimensional parameter spaces with computationally expensive or topologically complex likelihood functions. In this work, we present a Machine Learning framework designed to emulate complex, often non-Gaussian likelihood landscapes using gradient-boosted regression trees (XGBoost). We discuss the advantages of the Machine Learning approach in terms of computational efficiency and the resolution of confidence regions, particularly in scenarios with complex correlations or "curved" degeneracies. We validate this methodology by applying it to a recent analysis on flavour anomalies in semileptonic B meson decays and discussing the adaptability of this framework to other phenomenological systems, such as axion-like particles or cosmology global fits. Finally, we utilise SHAP (Shapley Additive exPlanations) values to provide a transparent analysis of feature importance, ensuring that the Machine Learning predictions remain physically interpretable and consistent with the underlying physics.
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±→K±ννˉ 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.
In HEP data analyses, finding an adequate function to model binned data has largely relied on a manual process: guess a functional form by intuition, fit, examine, then repeat until successful. We show that this iterative process can be automated by a machine using symbolic regression, which performs a data-driven search over function space without requiring prior knowledge of what an adequate function should look like. We present the SymbolFit package, which pairs symbolic regression with uncertainty modeling to target HEP analysis use cases, and demonstrate it on the CMS and ATLAS Run 2 dijet spectra: 560 independent seeded runs across seven simple fit configurations generated over 1000 functions fitting the spectra with χ2/NDF≈1, and 111 of the runs rediscovered the very dijet and UA2 functions used in published dijet searches.
Prototype-based explanations offer an intuitive, example-based approach to support the interpretability of machine learning black box classifiers but often lack feature-level granularity. We introduce a framework that integrates feature importance at two levels to address this gap. First, for local explanations, we propose \textit{alike parts}: a method that uses feature importance scores to highlight the most relevant, shared feature subsets between a classified instance and its nearest prototype, guiding user attention. Second, we augment the global prototype selection objective function with a feature importance term to actively promote diversity in the feature attributions of the selected prototypes. Experiments on six benchmark datasets show that this augmented selection process maintains or, in some cases, increases the prediction fidelity of the surrogate model, suggesting that feature diversity does not compromise model fidelity.