Data-driven Approach for Interpolation of Sparse Data

Extracting information about hadron resonances requires fitting theoretical models to experimental data. However, this data often comes from different experiments of different physics quantities in varying kinematic regions; studying coupled channels with different kinematic coverages and binning can make direct comparison challenging. The consistency of these datasets directly impacts the quality of the fit, thus making it difficult to accurately constrain the theoretical models. Sparse datasets in key kinematic regions further complicates the quantification of uncertainties, often requiring arbitrary weighting that may introduce bias. A robust approach to solving these problems involves utilising Gaussian Processes (GPs), a Bayesian inference machine learning technique that provides probabilistic predictions for unknown datapoints. Unlike traditional machine learning methods, GPs do not require any training; instead, they operate on three fundamental assumptions: 1. Some kernel function can be defined to measure the covariance between known datapoints; 2. This same kernel function can be used to predict the covariance between unknown datapoints; 3. Some idea of the form of the posterior distribution is known (e.g.