Model selection and signal extraction using Gaussian Process regression
Abhijith Gandrakota (Fermi National Accelerator Laboratory, Batavia, IL, USA); Amit Lath (Department of Physics & Astronomy, Rutgers, The State University of New Jersey, 136 Frelinghuysen Rd., Piscataway, NJ, USA); Alexandre Morozov (Department of Physics & Astronomy, Rutgers, The State University of New Jersey, 136 Frelinghuysen Rd., Piscataway, NJ, USA); Sindhu Murthy (Department of Physics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA, USA)
We present a novel computational approach for extracting localized signals from smooth background distributions. We focus on datasets that can be naturally presented as binned integer counts, demonstrating our procedure on the CERN open dataset with the Higgs boson signature, from the ATLAS collaboration at the Large Hadron Collider. Our approach is based on Gaussian Process (GP) regression — a powerful and flexible machine learning technique which has allowed us to model the background without specifying its functional form explicitly and separately measure the background and signal contributions in a robust and reproducible manner. Unlike functional fits, our GP-regression-based approach does not need to be constantly updated as more data becomes available. We discuss how to select the GP kernel type, considering trade-offs between kernel complexity and its ability to capture the features of the background distribution. We show that our GP framework can be used to detect the Higgs boson resonance in the data with more statistical significance than a polynomial fit specifically tailored to the dataset. Finally, we use Markov Chain Monte Carlo (MCMC) sampling to confirm the statistical significance of the extracted Higgs signature.
