SCALABLE BAYESIAN ADDITIVE MODELS FOR STELLAR FLARE DETECTION VIA AMORTIZED GAUSSIAN PROCESS INFERENCE AND HIDDEN MARKOV MODELS

Gaussian Processes (GPs) are essential for modeling complex time-series data in astronomy, such as quasi-periodic stellar rotation. However, exact GP inference scales cubically with the number of data points, creating a significant computational bottleneck for hierarchical or additive models. This paper investigates whether a deep generative surrogate can replace the exact GP kernel to enable faster, scalable Bayesian inference without sacrificing structural fidelity.

The authors propose a framework that utilizes a Variational Autoencoder (VAE) to learn a compressed, low-dimensional representation of the GP prior. By training the VAE on synthetic data generated from the Celerite kernel—a specialized, linear-time GP solver—the model learns to map stochastic dependencies into an isotropic latent space. During inference, the pre-trained decoder acts as a deterministic surrogate, bypassing expensive matrix inversions and covariance operations. The authors embed this VAE surrogate into an additive VAE+HMM (Hidden Markov Model) architecture to detect stellar flares in TESS light curve data, comparing its performance and computational efficiency against the exact Celerite+HMM framework.

The study demonstrates that the VAE surrogate accurately reproduces the structural characteristics of the exact Celerite kernel while drastically reducing computational overhead. By shifting the heavy lifting to an offline training phase, the resulting VAE+HMM architecture allows for rapid, large-scale characterization of stellar flares. The authors show that this methodology maintains high fidelity in isolating stochastic flare events from complex, quasi-periodic background rotation, providing a robust and efficient alternative for analyzing massive astrophysical datasets.