Tackling the noisy truncated moment problem with Gaussian Processes: An application to parton distribution functions
Abstract
In this work, we study the noisy truncated Hausdorff moment problem in the context of recovering parton distribution functions (PDFs) from their moments. We start by reviewing basics of the Hausdorff moment problem and analyze how the relation between the amount of moment data provided and the ability for f(x) to be reconstructed varies across different classes of parton distribution functions; we then turn to using Bayesian methods centered around Gaussian Processes (GPs) to solve the moment problems. Standard aspects of Bayesian regression such as covariance kernel choice, analytical characterization of the posterior, hyperparameter sampling with Monte Carlo methods, and validation metrics are detailed. In addition to this, powerful novel tools, such as a method to correct for mean bias in posterior distributions, and a simple class of covariance kernels whose x correlation length is learned during sampling are introduced. Finally, we test our framework on 5 datasets from valence, gluon, and sea quark phenomenological pion and nucleon PDF datasets, selected to reflect diversity in PDF behavior. We find that our GP framework robustly reconstructs PDFs given a moderate number of moments. Additionally, the novel tools developed in this work resolve persistent issues that would be difficult to address via conventional means. The presented framework can be readily applied to moments obtained via lattice Quantum Chromodynamics (LQCD) to reconstruct PDFs from theoretical first principles.
Related
- Convergence of stationary distributions for a class of zero-range processes and its application to a wealth distribution model with debt
- Optimizing Wigner Negativity in Scattering Processes Using Energetic Cost Functions
- Unconditional authentication in quantum key distribution via hybrid entangled physical unclonable functions
- Stochastic thermodynamics and predictability of Ornstein-Uhlenbeck processes: an application to the Madden-Julian Oscillation
- Resolving Local Structure of Distribution Functions in Collider Measurements
BibTeX
@misc{karur2026tackling,
title = {{Tackling the noisy truncated moment problem with Gaussian Processes: An application to parton distribution functions}},
author = {Rohith Karur},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23196},
eprint = {2609.23196},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23196},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tackling the noisy truncated moment problem with Gaussian Processes: An application to parton distribution functions
AU - Rohith Karur
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23196
UR - https://arxiv.org/abs/2609.23196
AB - In this work, we study the noisy truncated Hausdorff moment problem in the context of recovering parton distribution functions (PDFs) from their moments. We start by reviewing basics of the Hausdorff moment problem and analyze how the relation between the amount of moment data provided and the ability for f(x) to be reconstructed varies across different classes of parton distribution functions; we then turn to using Bayesian methods centered around Gaussian Processes (GPs) to solve the moment problems. Standard aspects of Bayesian regression such as covariance kernel choice, analytical characterization of the posterior, hyperparameter sampling with Monte Carlo methods, and validation metrics are detailed. In addition to this, powerful novel tools, such as a method to correct for mean bias in posterior distributions, and a simple class of covariance kernels whose x correlation length is learned during sampling are introduced. Finally, we test our framework on 5 datasets from valence, gluon, and sea quark phenomenological pion and nucleon PDF datasets, selected to reflect diversity in PDF behavior. We find that our GP framework robustly reconstructs PDFs given a moderate number of moments. Additionally, the novel tools developed in this work resolve persistent issues that would be difficult to address via conventional means. The presented framework can be readily applied to moments obtained via lattice Quantum Chromodynamics (LQCD) to reconstruct PDFs from theoretical first principles.
ER -