  With the advancement of technology, machine learning-based analytical methods
have pervaded nearly every discipline in modern studies. Particularly, a number
of methods have been employed to estimate the redshift of gamma-ray loud active
galactic nuclei (AGN), which are a class of supermassive black hole systems
known for their intense multi-wavelength emissions and violent variability.
Determining the redshifts of AGNs is essential for understanding their
distances, which, in turn, sheds light on our current understanding of the
structure of the nearby universe. However, the task involves a number of
challenges such as the need for meticulous follow-up observations across
multiple wavelengths and astronomical facilities. In this study, we employ a
simple yet effective deep learning model with a single hidden layer having $64$
neurons and a dropout of 0.25 in the hidden layer, on a sample of AGNs with
known redshifts from the latest AGN catalog, 4LAC-DR3, obtained from Fermi-LAT.
We utilized their spectral, spatial, and temporal properties to robustly
predict the redshifts of AGNs as well quantify their associated uncertainties,
by modifying the model using two different variational inference methods. We
achieve a correlation coefficient of 0.784 on the test set from the frequentist
model and 0.777 and 0.778 from both the variants of variational inference, and,
when used to make predictions on the samples with unknown redshifts, we achieve
mean predictions of 0.421, 0.415 and 0.393, with standard deviations of 0.258,
0.246 and 0.207 from the models, respectively.
