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Extracting knowledge from high-dimensional data has been notoriously difficult, primarily due to the so-called "curse of dimensionality" and the complex joint distributions of these dimensions. This is a particularly profound issue for high-dimensional gravitational wave data analysis where one requires to conduct Bayesian inference and estimate joint posterior distributions. In this study, we incorporate prior physical knowledge by sampling from desired interim distributions to develop the training dataset. Accordingly, the more relevant regions of the high-dimensional feature space are covered by additional data points, such that the model can learn the subtle but important details. We adapt the normalizing flow method to be more expressive and trainable, such that the information can be effectively extracted and represented by the transformation between the prior and target distributions. Once trained, our model only takes approximately 1 s on one V100 GPU to generate thousands of samples for probabilistic inference purposes. The evaluation of our approach confirms the efficacy and efficiency of gravitational wave data inferences and points to a promising direction for similar research. The source code, specifications, and detailed procedures are publicly accessible on GitHub.


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Sampling with Prior Knowledge for High-dimensional Gravitational Wave Data Analysis

Show Author's information He WangZhoujian CaoYue ZhouZong-Kuan GuoZhixiang Ren( )
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China
Department of Astronomy, Beijing Normal University, Beijing 100875, China
Department of Networked Intelligence, Peng Cheng Laboratory, Shenzhen 518055, China

Abstract

Extracting knowledge from high-dimensional data has been notoriously difficult, primarily due to the so-called "curse of dimensionality" and the complex joint distributions of these dimensions. This is a particularly profound issue for high-dimensional gravitational wave data analysis where one requires to conduct Bayesian inference and estimate joint posterior distributions. In this study, we incorporate prior physical knowledge by sampling from desired interim distributions to develop the training dataset. Accordingly, the more relevant regions of the high-dimensional feature space are covered by additional data points, such that the model can learn the subtle but important details. We adapt the normalizing flow method to be more expressive and trainable, such that the information can be effectively extracted and represented by the transformation between the prior and target distributions. Once trained, our model only takes approximately 1 s on one V100 GPU to generate thousands of samples for probabilistic inference purposes. The evaluation of our approach confirms the efficacy and efficiency of gravitational wave data inferences and points to a promising direction for similar research. The source code, specifications, and detailed procedures are publicly accessible on GitHub.

Keywords:

high-dimensional data, prior sampling, normalizing flow, gravitational wave
Received: 22 July 2021 Revised: 13 October 2021 Accepted: 14 October 2021 Published: 27 December 2021 Issue date: March 2022
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Publication history

Received: 22 July 2021
Revised: 13 October 2021
Accepted: 14 October 2021
Published: 27 December 2021
Issue date: March 2022

Copyright

© The author(s) 2022

Acknowledgements

The research was supported by the Peng Cheng Laboratory Cloud Brain (No. PCL2021A13), the National Natural Science Foundation of China (Nos. 11721303, 12075297, and 11690021), and the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA1502110202). This research has made use of data, software, and/or web tools obtained from the gravitational-wave Open Science Center, a service of LIGO Laboratory, the LIGO Scientific Collaboration, and the Virgo Collaboration.

This work was implemented in PYTHON and used NUMPY[52], SCIPY[53], PANDAS[54], IMBALANCED-LEARN[14], DYNESTY[55], NFLOWS[41], PYTORCH[40] and MATPLOTLIB[56]. Gravitational wave waveforms were generated using BILBY[34,35]. Figures were prepared using MATPLOTLIB[56], SCIENCEPLOTS[57], and CORNER[51].

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