  Precise measurements of the black hole mass are essential to gain insight on
the black hole and host galaxy co-evolution. A direct measure of the black hole
mass is often restricted to nearest galaxies and instead, an indirect method
using the single-epoch virial black hole mass estimation is used for objects at
high redshifts. However, this method is subjected to biases and uncertainties
as it is reliant on the scaling relation from a small sample of local active
galactic nuclei. In this study, we propose the application of conformalised
quantile regression (CQR) to quantify the uncertainties of the black hole
predictions in a machine learning setting. We compare CQR with various
prediction interval techniques and demonstrated that CQR can provide a more
useful prediction interval indicator. In contrast to baseline approaches for
prediction interval estimation, we show that the CQR method provides prediction
intervals that adjust to the black hole mass and its related properties. That
is it yields a tighter constraint on the prediction interval (hence more
certain) for a larger black hole mass, and accordingly, bright and broad
spectral line width source. Using a combination of neural network model and CQR
framework, the recovered virial black hole mass predictions and uncertainties
are comparable to those measured from the Sloan Digital Sky Survey. The code is
publicly available at https://github.com/yongsukyee/uncertain_blackholemass.
