Lecture notes on Machine Learning applications for global fits

TL;DR

This paper presents a comprehensive framework using modern Machine Learning surrogates for efficient global fits in high-energy physics, including techniques like Boosted Decision Trees, active learning, and interpretability tools, applied to ALP parameter exploration.

Contribution

It introduces a robust ML workflow for global fits, combining surrogate modeling, active learning, hyperparameter tuning, interpretability, and application to a real physics anomaly.

Findings

ML surrogates significantly reduce computational costs.

The workflow enables efficient exploration of ALP parameter space.

Application to Belle II anomaly demonstrates practical effectiveness.

Abstract

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 $B^\pm \to K^\pm \nu \bar{\nu}$ 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.