Use of Supervised Machine Learning for determination of redshifts of Gamma-ray Bursts

Gamma-ray bursts (GRBs) by virtue of their high luminosities are observed up to redshift z=9.4 (Cucchiara et al. 2011), far beyond the most distant quasars orgalaxies. and thus have the potential to be vital cosmological probes of earlier processes in theuniverse, such as reionization, evolution of the star formation rate (SFR), in general, and formation of the firstgeneration (Population III) stars. This requires a relatively large sample of GRBs with knownredshifts and well defined observational selection effects. Most GRB instruments provide sampleswith a well defined prompt gamma-ray peak flux threshold. However, samples with redshift, requiringlocalization at X-rays and optical-UV follow up observations, suffer from more complex truncations,which hampers the progress to this end. The Swift satellite, the most successful instruments formeasuring spectroscopic redshifts of GRBs, has provided redshifts only about one-third of GRBs itdetected. The situation is even less promising for other instruments. Thus, for more than 20 yearsthere have been attempts to increase the number of GRBs with known z via a theoretical estimate ofredshift (so called pseudo-redshifts) using GRB relations, but these approaches have led toinaccurate predictions. Thus, we adopt here supervised machine learning approaches to estimateredshifts for GRBs using existing data from many instruments; Swift-(BAT,XRT), Fermi-GBM andKonus-Wind. These methods will also allow us to estimate possible non-linear relations between the redshift andother GRB characteristics. Our approach brings a novelty on this research area,because, for the first time, it adds the afterglow plateau emission characteristics. Weobtained best results using the ``generalized additive" model with a correlation coefficient of0.91 between the predicted and the observed redshifts and an overall dispersion of $0.2$.The addition of afterglow parameters improves the predictions by 45% compared to previous resultsin the published literature. We also show that using the predicted redshifts we obtaindistributions and cosmological evolutions very similar to those obtained from actual measuredredshifts.