Uncertainty Quantification of the Virial Black Hole Mass with Conformal Prediction

TL;DR

This paper introduces the use of conformalised quantile regression (CQR) to accurately quantify uncertainties in virial black hole mass estimates, improving prediction intervals over traditional methods in a machine learning context.

Contribution

The study applies CQR to black hole mass estimation, demonstrating its ability to produce adaptive, tighter prediction intervals that reflect the properties of the black hole and spectral data.

Findings

CQR provides more useful, adaptive prediction intervals.

Prediction intervals tighten for larger black hole masses.

The method yields mass predictions comparable to SDSS measurements.

Abstract

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.