Deep Neural Networks for Estimation of Gamma-Ray Burst Redshifts

While the available set of Gamma-ray Burst (GRB) data with known redshift is currently limited, a much larger set of GRB data without redshift is available from different instruments. This data includes well-measured prompt gamma-ray flux and spectral information. We estimate the redshift of a selection of these GRBs detected by Fermi-GBM and Konus-Wind using Machine Learning techniques that are based on spectral parameters. We find that Deep Neural Networks with Random Forest models employing non-linear relations among input parameters can reasonably reproduce the pseudo-redshift distribution of GRBs, mimicking the distribution of GRBs with spectroscopic redshift. Furthermore, we find that the pseudo-redshift samples of GRBs satisfy (i) Amati relation between the peak photon energy of the time-averaged energy spectrum in the cosmological rest frame of the GRB ${E}_{\rm i, p}$ and the isotropic-equivalent radiated energy ${E}_{\rm iso}$ during the prompt phase; and (ii) Yonetoku relation between ${E}_{\rm i, p}$ and isotropic-equivalent luminosity ${L}_{\rm iso}$, both measured during the peak flux interval.