Model-independent calibrations of gamma-ray bursts using machine learning

We alleviate the circularity problem, whereby gamma-ray bursts are not perfect distance indicators, by means of a new model-independent technique based on B\'ezier polynomials. To do so, we use the well consolidate \textit{Amati} and \textit{Combo} correlations. We consider improved calibrated catalogs of mock data from differential Hubble rate points. To get our mock data, we use those machine learning scenarios that well adapt to gamma ray bursts, discussing in detail how we handle small amounts of data from our machine learning techniques. In particular, we explore only three machine learning treatments, i.e. \emph{linear regression}, \emph{neural network} and \emph{random forest}, emphasizing quantitative statistical motivations behind these choices. Our calibration strategy consists in taking Hubble's data, creating the mock compilation using machine learning and calibrating the aforementioned correlations through B\'ezier polynomials with a standard chi-square analysis first and then by means of a hierarchical Bayesian regression procedure. The corresponding catalogs, built up from the two correlations, have been used to constrain dark energy scenarios. We thus employ Markov Chain Monte Carlo numerical analyses based on the most recent Pantheon supernova data, baryonic acoustic oscillations and our gamma ray burst data. We test the standard $\Lambda$CDM model and the Chevallier-Polarski-Linder parametrization. We discuss the recent $H_0$ tension in view of our results. Moreover, we highlight a further severe tension over $\Omega_m$ and we conclude that a slight evolving dark energy model is possible.