Generalized Approach to Matched Filtering using Neural Networks-猫眼课题宝

DOI：

10.1103/physrevd.105.043006

发表时间：

2021-04

期刊：

ArXiv

影响因子：

通讯作者：

中科院分区：

其他

文献类型：

作者：

Jingkai Yan;Mariam Avagyan;R. Colgan;D. Veske;I. Bartos;John N. Wright;Z. M'arka;S. M'arka

引力波科学是一个开创性的领域，目前正在吸收和发明深度学习技术，并迅速发展数据分析方法。该领域的大部分复杂的旗舰搜索依赖于其核心中久经考验的匹配过滤原则。在本文中，我们对新兴的深度学习与传统技术之间的关系进行了关键的观察：匹配滤波在形式上等价于一个特定的神经网络。这意味着可以解析地构建神经网络以准确地实现匹配过滤，并且可以对数据进行进一步的训练或增加额外的复杂性以提高性能。此外，我们还表明，无论是否知道参数分布的先验信息，所提出的神经网络结构的性能都优于匹配滤波。当先验条件给定时，所提出的神经网络可以逼近统计最优性能。我们还提出并研究了两种不同的神经网络结构MNet-Short和MNet-Deep，这两种网络结构都是在初始化时实现匹配滤波，并且都可以对数据进行训练。Mnet-Short的结构更简单，而MNet-Deep则更灵活，可以处理更广泛的分布。使用真实的LIGO数据和合成注入的实验证实了我们的理论发现，在假阳性率大于$5×10^-3}$的情况下，我们提出的方法明显优于匹配滤波。匹配滤波和神经网络之间的基本等价性使我们可以定义一个“复杂性标准蜡烛”，以表征在共同框架中搜索引力波信号的不同方法的相对复杂性。最后，我们的结果对深度学习在引力波探测中的作用提出了新的观点。

Gravitational wave science is a pioneering field with rapidly evolving data analysis methodology currently assimilating and inventing deep learning techniques. The bulk of the sophisticated flagship searches of the field rely on the time-tested matched filtering principle within their core. In this paper, we make a key observation on the relationship between the emerging deep learning and the traditional techniques: matched filtering is formally equivalent to a particular neural network. This means that a neural network can be constructed analytically to exactly implement matched filtering, and can be further trained on data or boosted with additional complexity for improved performance. Moreover, we show that the proposed neural network architecture can outperform matched filtering, both with or without knowledge of a prior on the parameter distribution. When a prior is given, the proposed neural network can approach the statistically optimal performance. We also propose and investigate two different neural network architectures MNet-Shallow and MNet-Deep, both of which implement matched filtering at initialization and can be trained on data. MNet-Shallow has simpler structure, while MNet-Deep is more flexible and can deal with a wider range of distributions. Our theoretical findings are corroborated by experiments using real LIGO data and synthetic injections, where our proposed methods significantly outperform matched filtering at false positive rates above $5\times 10^{-3}\%$. The fundamental equivalence between matched filtering and neural networks allows us to define a"complexity standard candle"to characterize the relative complexity of the different approaches to gravitational wave signal searches in a common framework. Finally, our results suggest new perspectives on the role of deep learning in gravitational wave detection.

Generalized Approach to Matched Filtering using Neural Networks

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