Fast and scalable Gaussian process modeling with applications to astronomical time series [IMA]

http://arxiv.org/abs/1703.09710


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 as the cube of the number of data points, their application has been limited to relatively small datasets. In this paper, we present a 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 is effective in many other cases. We present a mathematical description of the method, the details of the implementation, and a comparison to existing scalable Gaussian Process methods. The method is flexible, fast, and most importantly, interpretable, with a wide 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.

Read this paper on arXiv…

D. Foreman-Mackey, E. Agol, R. Angus, et. al.
Thu, 30 Mar 17
29/69

Comments: Submitted to the AAS Journals. Comments welcome. Code available: this https URL