# Fast and scalable Gaussian process modeling with applications to astronomical time series

## TL;DR

This paper introduces a new linear-scaling Gaussian Process method for one-dimensional data, enabling efficient probabilistic analysis of large astronomical time series without requiring evenly spaced observations.

## Contribution

The paper presents a novel Gaussian Process modeling approach with linear computational complexity for 1D data, applicable to large astronomical datasets and based on covariance functions as mixtures of complex exponentials.

## Key findings

- Method scales linearly with dataset size
- Successfully applied to simulated and real astronomical data
- Provides interpretable probabilistic inference

## Abstract

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose but, since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small datasets. In this paper, we present a novel method for Gaussian Process modeling in one-dimension where the computational requirements scale linearly with the size of the dataset. We demonstrate the method by applying it to simulated and real astronomical time series datasets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically-driven damped harmonic oscillators -- providing a physical motivation for and interpretation of this choice -- but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable Gaussian Process methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.