Uncertainty Quantification of the Virial Black Hole Mass with Conformal Prediction
This work addresses uncertainty quantification for black hole mass estimates in astrophysics, providing a more reliable method for high-redshift studies, though it is incremental as it applies an existing technique to a specific domain problem.
The study tackled the problem of quantifying uncertainties in virial black hole mass predictions, which are biased due to reliance on small local samples, by applying conformalised quantile regression (CQR) in a machine learning setting, resulting in prediction intervals that adjust to black hole properties and are comparable to Sloan Digital Sky Survey measurements.
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.