Split-N-Fit: A Differentiable Maximum Likelihood Fit for training neural networks and performing anomaly detection on data

In particle physics, machine learning algorithms are often trained on simulations to codify a selection algorithm or perform a reconstruction task. When these algorithms are then applied to recorded data, their performance incurs a cost in terms of modeling uncertainties due to the limitations of the simulation. Training on data would resolve this issue, but existing approaches require regions with high sample purity, which are nearly impossible to obtain. Instead, we present an approach to construct a fully differentiable maximum likelihood fit, enabling differentiable hypothesis testing directly in data. Our approach, dubbed Split-N-Fit can adapt to all forms of hypothesis tests and includes the ability to model systematic uncertainties. We demonstrate the use of Split-N-Fit in particle physics, specifically covering simulation mismodeling in a supervised measurement of the di-Higgs boson. We find that our approach outperforms conventional supervised learning approaches when trained on samples that are mismodeled w.r.t reference samples, and that Split-N-Fit adapts to these "poor'' training data, achieving near-optimal performance.