Uncertainty quantification of the virial black hole mass with conformal prediction

Journal Article · 13 July 2023 · Monthly Notices of the Royal Astronomical Society

DOI: https://doi.org/10.1093/mnras/stad2080 · OSTI ID:1991977

Yong, Suk Yee  ^[1]; Ong, Cheng Soon  ^[2]

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1. ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D) (Australia); Macquarie University, Sydney, NSW (Australia); Commonwealth Scientific and Industrial Research Organisation (CSIRO) (Australia)
2. Commonwealth Scientific and Industrial Research Organisation (CSIRO), Canberra, ACT (Australia); Australian National Univ., Canberra, ACT (Australia)

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 conformalized 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.

• Research Organization: US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Sloan Digital Sky Survey (SDSS)
• Sponsoring Organization: Alfred P. Sloan Foundation; USDOE; USDOE Office of Science (SC)
• OSTI ID: 1991977
• Journal Information: Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Journal Issue: 2 Vol. 524; ISSN 0035-8711; ISSN 1365-2966
• Publisher: Oxford University PressCopyright Statement
• Country of Publication: United States
• Language: English