Generalized Approach to Matched Filtering using Neural Networks. (arXiv:2104.03961v2 [astro-ph.IM] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Yan_J/0/1/0/all/0/1">Jingkai Yan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Avagyan_M/0/1/0/all/0/1">Mariam Avagyan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Colgan_R/0/1/0/all/0/1">Robert E. Colgan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Veske_D/0/1/0/all/0/1">Doğa Veske</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bartos_I/0/1/0/all/0/1">Imre Bartos</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wright_J/0/1/0/all/0/1">John Wright</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Marka_Z/0/1/0/all/0/1">Zsuzsa Márka</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Marka_S/0/1/0/all/0/1">Szabolcs Márka</a>
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 $5times 10^{-3}%$. 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.
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 $5times 10^{-3}%$. 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.
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