For fixed sound-horizon and supernova calibrations, no late-time modification—even one violating cosmic distance duality—can resolve the Hubble tension, because the required ~8-10% CDDR violation is excluded by BAO, cosmic-chronometer, and CMB spectral constraints.
An Intuitive Tutorial to Gaussian Process Regression
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abstract
This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify uncertainty over predictions. The tutorial starts with explaining the basic concepts that a Gaussian process is built on, including multivariate normal distribution, kernels, non-parametric models, and joint and conditional probability. It then provides a concise description of GPR and an implementation of a standard GPR algorithm. In addition, the tutorial reviews packages for implementing state-of-the-art Gaussian process algorithms. This tutorial is accessible to a broad audience, including those new to machine learning, ensuring a clear understanding of GPR fundamentals.
fields
astro-ph.CO 1years
2026 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
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Can Distance Duality Violation Save Late-time Solutions to the Hubble Tension?
For fixed sound-horizon and supernova calibrations, no late-time modification—even one violating cosmic distance duality—can resolve the Hubble tension, because the required ~8-10% CDDR violation is excluded by BAO, cosmic-chronometer, and CMB spectral constraints.