# Lecture notes on Machine Learning applications for global fits

arXiv: https://arxiv.org/abs/2604.07520 · HTML: https://mlsanity.com/paper/2604.07520/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [A Framework for Interdomain and Multioutput Gaussian Processes](https://mlsanity.com/paper/2003.01115/) (2020)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [Active Learning and Bayesian Optimization: a Unified Perspective to Learn with a Goal](https://mlsanity.com/paper/2303.01560/) (2023)

## Built on by (most cited first, 1 of 1)

- [Physically Consistent Parameter Inference: Transparent Machine Learning Emulation in High Energy Physics and Cosmology](https://mlsanity.com/paper/2607.12726/) (2026)

## Abstract (arXiv)

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^± nu barnu 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.