Fast and Scalable Gaussian Process Modeling with Applications to Astronomical Time Series

By Daniel Foreman-Mackey, E. Agol, Sivaram Ambikasaran, R. Angus. 2017

640 citations recorded by the source corpus.

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large data sets. Gaussian processes (GPs) 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 data sets. In this paper, we present a novel method for GPs modeling in one dimension where the computational requirements scale linearly with the size of the data set. We demonstrate the method by applying it to simulated and real astronomical time series data sets. 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 GP 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.

Subfields: Artificial Intelligence, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/f019e9a4ac3409614a269775f66a3df1f454d58d

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Citations in the corpus

Inferring probabilistic stellar rotation periods using Gaussian processes (2017, methodology): “celerite, a new method for rapid computation of the ‘solve’ and determinant calculations of covariance matrices necessary for GP inference has recently been developed (Foreman-Mackey et al. 2017).”
A Kinematical Detection of Two Embedded Jupiter-mass Planets in HD 163296 (2018, background): “This approach removes the need to assume an analytical form for the function, providing more flexibility in the model in addition to not requiring the binning of data (Foreman-Mackey et al. 2017).”