Physically Consistent Parameter Inference: Transparent Machine-Learning Emulation in High Energy Physics and Cosmology

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 of flavour anomalies in semileptonic B meson decays and discussing the adaptability of the framework to other phenomenological systems, such as axion-like particles and global fits in cosmology. 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.