Scalable Bayesian Additive Models for Stellar Flare Detection via Amortized Gaussian Process Inference and Hidden Markov Models

2026-06-21

AI Summary

This work addresses the computational bottleneck of Gaussian process models—such as Celerite—in Bayesian analysis of long astronomical time series, particularly for stellar flare detection, where complex additive structures incur prohibitive inference costs. The authors propose a generative surrogate framework that, for the first time, integrates a variational autoencoder (VAE) as an amortized proxy within a Bayesian additive model. The VAE learns a low-dimensional, isotropic representation of the Celerite prior, replacing expensive covariance computations with efficient neural network forward passes. Coupled with a hidden Markov model (HMM), this architecture enables scalable approximate inference. Experiments on real astronomical data demonstrate that the VAE+HMM approach substantially reduces computational overhead while faithfully preserving the exact kernel structure and achieving competitive flare detection performance, thereby enabling large-scale stellar flare surveys.

Abstract

Gaussian Processes (GPs) are a powerful tool for Bayesian time-series modeling, yet their cubic computational cost remains a severe barrier for application to long, high-cadence datasets in astronomy. While specialized scalable solvers like Celerite elegantly reduce this scaling to linear time, repeatedly evaluating the exact likelihood during iterative Bayesian sampling is a bottleneck for developing more complex models, like hierarchical or additive models in which Celerite is only one component. To make this inference computationally tractable, we introduce a generative surrogate framework. By utilizing a Variational Autoencoder (VAE) to learn a compressed representation of the Celerite prior, we map highly correlated stochastic dependencies into a low-dimensional, isotropic manifold. This transition completely bypasses exact covariance operations, shifting the computational burden to a rapid neural network forward pass. Through an extensive simulation study, we show that the generative surrogate accurately reproduces the structural fidelity of exact physical kernels like Celerite. Finally, we demonstrate embedding our VAE approximation into an additive model that combines Celerite and a hidden Markov model (HMM) for stellar flare detection in time series data of stars. We evaluate the joint VAE+HMM architecture against the exact Celerite+HMM framework on empirical astrophysical time series and demonstrate that the proposed methodology achieves significant reductions in computational time, enabling the rigorous, large-scale characterization of stellar flares across massive data archives.

Problem

• stellar flare detection
• Gaussian Processes
• scalable inference
• Bayesian additive models
• computational bottleneck

Innovation

• Amortized Inference
• Gaussian Process Surrogate
• Variational Autoencoder
• Scalable Bayesian Modeling
• Stellar Flare Detection