Shared Stochastic Gaussian Process Latent Variable Models: A Multi-modal Generative Model for Quasar Spectra

TL;DR

This paper introduces a scalable multi-modal Gaussian process model that jointly learns to generate quasar spectra and their scientific properties, handling missing data and enabling high-fidelity reconstructions in astrophysics.

Contribution

It extends stochastic variational GPLVMs to multi-observation spaces, allowing simultaneous generation of spectra and labels with shared latent variables, and manages missing data effectively.

Findings

High-quality spectral and label reconstructions achieved

Model handles missing data across observation spaces

Demonstrates scientific interpretability of the generative process

Abstract

This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both observed spectral features and scientific properties of astrophysical objects such as galaxies or exoplanets. In our application, we study the spectra of very luminous galaxies known as quasars, along with their properties, such as the mass of their central supermassive black hole, accretion rate, and luminosity-resulting in multiple observation spaces. A single data point is then characterized by different classes of observations, each with different likelihoods. Our proposed model extends the baseline stochastic variational Gaussian process latent variable model (GPLVM) introduced by Lalchand et al. (2022) to this setting, proposing a seamless generative model where the quasar spectra and scientific labels can be generated simultaneously using a shared latent space as input to different sets of Gaussian process decoders, one for each observation space. Additionally, this framework enables training in a missing data setting where a large number of dimensions per data point may be unknown or unobserved. We demonstrate high-fidelity reconstructions of the spectra and scientific labels during test-time inference and briefly discuss the scientific interpretations of the results, along with the significance of such a generative model.