# Inferring Black Hole Properties from Astronomical Multivariate Time Series with Bayesian Attentive Neural Processes

arXiv: https://arxiv.org/abs/2106.01450 · HTML: https://mlsanity.com/paper/2106.01450/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 2 Jun 2021.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Hierarchical Inference With Bayesian Neural Networks: An Application to Strong Gravitational Lensing](https://mlsanity.com/paper/2010.13787/) (2020)
- [Large-Scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant](https://mlsanity.com/paper/2012.00042/) (2020)
- [AGNet: Weighing Black Holes with Machine Learning](https://mlsanity.com/paper/2011.15095/) (2020)

## Built on by (most cited first, 4 of 4)

- [DeepGraviLens: a Multi-Modal Architecture for Classifying Gravitational Lensing Data](https://mlsanity.com/paper/2205.00701/) (2022)
- [Inferring Structural Parameters of Low-Surface-Brightness-Galaxies with Uncertainty Quantification using Bayesian Neural Networks](https://mlsanity.com/paper/2207.03471/) (2022)
- [Virgo: Scalable Unsupervised Classification of Cosmological Shock Waves](https://mlsanity.com/paper/2208.06859/) (2022)
- [Probabilistic Data-Driven Modelling of Astrophysical Transients: The Neural Process Family for Ultrafast and Class-Agnostic Light Curve Reconstruction with NightLANP](https://mlsanity.com/paper/2605.27527/) (2026)

## Abstract (arXiv)

Among the most extreme objects in the Universe, active galactic nuclei (AGN) are luminous centers of galaxies where a black hole feeds on surrounding matter. The variability patterns of the light emitted by an AGN contain information about the physical properties of the underlying black hole. Upcoming telescopes will observe over 100 million AGN in multiple broadband wavelengths, yielding a large sample of multivariate time series with long gaps and irregular sampling. We present a method that reconstructs the AGN time series and simultaneously infers the posterior probability density distribution (PDF) over the physical quantities of the black hole, including its mass and luminosity. We apply this method to a simulated dataset of 11,000 AGN and report precision and accuracy of 0.4 dex and 0.3 dex in the inferred black hole mass. This work is the first to address probabilistic time series reconstruction and parameter inference for AGN in an end-to-end fashion.