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arXiv 1703.09710astro-ph.IMastro-ph.EPastro-ph.SRphysics.data-anstat.AP
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快速可扩展高斯过程建模及其在天文时间序列中的应用

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

Daniel Foreman-Mackey, Eric Agol, Sivaram Ambikasaran, Ruth Angus

摘要:

大规模时域天文学领域的不断发展需要概率数据分析的方法,这些方法在计算上是易于处理的,即使是大型数据集。高斯过程是用于此目的的一类流行的模型,但由于计算成本通常是数据点数量的立方,因此其应用仅限于小数据集。在本文中,我们提出了一种新的方法在一维高斯过程建模的计算需求与数据集的大小线性缩放。我们通过将其应用于模拟和真实的天文时间序列数据集来演示该方法。这些演示是恒星自转周期、星震振荡谱和凌日行星参数的概率推断的例子。当协方差函数表示为复指数的混合时,该方法利用问题中的结构,而不需要均匀间隔的观测或均匀噪声。这种形式的协方差自然出现时,该过程是一个随机驱动的阻尼谐振子的混合物-提供了一个物理动机和解释这种选择-但我们也表明,它可以是一个有用的有效模型在其他一些情况下。我们提出了一个数学描述的方法,并将其与现有的可扩展高斯过程方法进行比较。该方法是快速和可解释的,在天文数据分析和超越的一系列潜在的应用。我们用C++、Python和Julia提供了该方法的经过充分测试和记录的开源实现。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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