Learning Bayes' theorem with a neural network for gravitational-wave inference

09/12/2019
by   Alvin J. K. Chua, et al.
NASA
0

We wish to achieve the Holy Grail of Bayesian inference with deep-learning techniques: training a neural network to instantly produce the posterior p(θ|D) for the parameters θ, given the data D. In the setting of gravitational-wave astronomy, we have access to a generative model for signals in noisy data (i.e., we can instantiate the prior p(θ) and likelihood p(D|θ)), but are unable to economically compute the posterior for even a single realization of D. Here we demonstrate how a network may be taught to estimate p(θ|D) regardless, by simply showing it numerous realizations of D.

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References

  • B. P. Abbott et al. (2019) Low-latency gravitational-wave alerts for multimessenger astronomy during the second advanced LIGO and virgo observing run. The Astrophysical Journal 875 (2), pp. 161. External Links: Document, Link Cited by: Introduction..
  • B. Abbott, R. Abbott, T. Abbott, S. Abraham, F. Acernese, K. Ackley, C. Adams, R. Adhikari, V. Adya, C. Affeldt, et al. (2019) Binary black hole population properties inferred from the first and second observing runs of advanced ligo and advanced virgo. arXiv:1811.12940. Cited by: Introduction..
  • K. G. Arun, A. Buonanno, G. Faye, and E. Ochsner (2009) Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: ready-to-use gravitational waveforms. Phys. Rev. D 79, pp. 104023. External Links: Document, Link Cited by: Leveraging reduced waveform representations..
  • J. Blackman, S. E. Field, C. R. Galley, B. Szilágyi, M. A. Scheel, M. Tiglio, and D. A. Hemberger (2015) Fast and Accurate Prediction of Numerical Relativity Waveforms from Binary Black Hole Coalescences Using Surrogate Models. Phys. Rev. Lett. 115, pp. 121102. External Links: Document, Link Cited by: Introduction..
  • P. Cañizares, S. E. Field, J. R. Gair, and M. Tiglio (2013) Gravitational wave parameter estimation with compressed likelihood evaluations. Phys. Rev. D 87, pp. 124005. External Links: Document, Link Cited by: Introduction..
  • N. Christensen and R. Meyer (1998) Markov chain monte carlo methods for bayesian gravitational radiation data analysis. Phys. Rev. D 58, pp. 082001. External Links: Document, Link Cited by: Introduction..
  • A. J. K. Chua, C. R. Galley, and M. Vallisneri (2019) Reduced-order modeling with artificial neurons for gravitational-wave inference. Phys. Rev. Lett. 122, pp. 211101. External Links: Document, Link Cited by: Introduction., Leveraging reduced waveform representations., Leveraging reduced waveform representations., Discussion..
  • J.D.E. Creighton and W.G. Anderson (2011) Gravitational-wave physics and astronomy: an introduction to theory, experiment and data analysis. Wiley Series in Cosmology, Wiley. External Links: ISBN 9783527408863, LCCN 2012554560, Link Cited by: Introduction..
  • K. Danzmann et al. (2017) Laser Interferometer Space Antenna. ArXiv e-prints. External Links: 1702.00786 Cited by: Introduction..
  • C. de Troyes, B. Raffel, and J. J. Duggan (1999) Perceval: the story of the grail. Yale University Press. External Links: ISBN 9780300075854, Link Cited by: footnote 1.
  • C. Dreissigacker, R. Sharma, C. Messenger, R. Zhao, and R. Prix (2019) Deep-learning continuous gravitational waves. Phys. Rev. D 100, pp. 044009. External Links: Document, Link Cited by: Introduction..
  • X. Fan, J. Li, X. Li, Y. Zhong, and J. Cao (2019) Applying deep neural networks to the detection and space parameter estimation of compact binary coalescence with a network of gravitational wave detectors. Science China Physics, Mechanics & Astronomy 62 (6), pp. 969512. External Links: ISSN 1869-1927, Document, Link Cited by: Introduction..
  • S. E. Field, C. R. Galley, F. Herrmann, J. S. Hesthaven, E. Ochsner, and M. Tiglio (2011) Reduced Basis Catalogs for Gravitational Wave Templates. Phys. Rev. Lett. 106, pp. 221102. External Links: Document, Link Cited by: Introduction., Leveraging reduced waveform representations..
  • S. E. Field, C. R. Galley, J. S. Hesthaven, J. Kaye, and M. Tiglio (2014) Fast Prediction and Evaluation of Gravitational Waveforms Using Surrogate Models. Phys. Rev. X 4, pp. 031006. External Links: Document, Link Cited by: Introduction..
  • H. Gabbard, M. Williams, F. Hayes, and C. Messenger (2018) Matching Matched Filtering with Deep Networks for Gravitational-Wave Astronomy. Phys. Rev. Lett. 120, pp. 141103. External Links: Document, Link Cited by: Introduction..
  • H. Gabbard, C. Messenger, I. S. Heng, F. Tonolini, and R. Murray-Smith (2019) Estimating bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy. arXiv preprint. Cited by: Introduction..
  • T. Gebhard, N. Kilbertus, G. Parascandolo, I. Harry, and B. Schölkopf (2017) ConvWave: Searching for Gravitational Waves with Fully Convolutional Neural Nets. In Workshop on Deep Learning for Physical Sciences (DLPS) at the 31st Conference on Neural Information Processing Systems (NIPS), External Links: Link Cited by: Introduction..
  • T. D. Gebhard, N. Kilbertus, I. Harry, and B. Schölkopf (2019) Convolutional neural networks: a magic bullet for gravitational-wave detection?. arXiv:1904.08693. Cited by: Introduction..
  • D. George and E. A. Huerta (2018) Deep neural networks to enable real-time multimessenger astrophysics. Phys. Rev. D 97, pp. 044039. External Links: Document, Link Cited by: Introduction..
  • D. George and E.A. Huerta (2018) Deep Learning for real-time gravitational wave detection and parameter estimation: Results with Advanced LIGO data. Physics Letters B 778, pp. 64 – 70. External Links: ISSN 0370-2693, Document, Link Cited by: Introduction..
  • I. Goodfellow, Y. Bengio, and A. Courville (2016) Deep learning. MIT Press. Cited by: Introduction., Training neural networks to produce posteriors..
  • P. Gregory (2005) Bayesian logical data analysis for the physical sciences: a comparative approach with mathematica® support. Cambridge University Press. External Links: ISBN 9781139444286, Link Cited by: Introduction..
  • M. Hannam, P. Schmidt, A. Bohé, L. Haegel, S. Husa, F. Ohme, G. Pratten, and M. Pürrer (2014) Simple model of complete precessing black-hole-binary gravitational waveforms. Phys. Rev. Lett. 113, pp. 151101. External Links: Document, Link Cited by: Introduction..
  • S. S. Haykin (1999) Neural networks: a comprehensive foundation. Prentice Hall. External Links: ISBN 9780132733502, LCCN gb98059240, Link Cited by: Introduction..
  • D. P. Kingma and J. Ba (2014) Adam: A Method for Stochastic Optimization. ArXiv e-prints. External Links: 1412.6980 Cited by: Example results..
  • P. G. Krastev (2019) Real-time detection of gravitational waves from binary neutron stars using artificial neural networks. arXiv:1908.03151. Cited by: Introduction..
  • Y. LeCun and Y. Bengio (1998) Convolutional networks for images, speech, and time series. In The Handbook of Brain Theory and Neural Networks, M. A. Arbib (Ed.), pp. 255–258. External Links: ISBN 0-262-51102-9, Link Cited by: Introduction..
  • LIGO Scientific Collaboration and Virgo Collaboration and others (2018) GWTC-1: a gravitational-wave transient catalog of compact binary mergers observed by ligo and virgo during the first and second observing runs. arXiv:1811.12907. Cited by: Introduction..
  • A. L. Maas, A. Y. Hannun, and A. Y. Ng (2013) Rectifier Nonlinearities Improve Neural Network Acoustic Models. In Proceedings of the 30th International Conference on Machine Learning, Cited by: Example results..
  • C. Messick, K. Blackburn, P. Brady, P. Brockill, K. Cannon, R. Cariou, S. Caudill, S. J. Chamberlin, J. D. E. Creighton, R. Everett, et al. (2017) Analysis framework for the prompt discovery of compact binary mergers in gravitational-wave data. Phys. Rev. D 95, pp. 042001. External Links: Document, Link Cited by: Introduction..
  • A. L. Miller, P. Astone, S. D’Antonio, S. Frasca, G. Intini, I. La Rosa, P. Leaci, S. Mastrogiovanni, F. Muciaccia, A. Mitidis, C. Palomba, O. J. Piccinni, A. Singhal, B. F. Whiting, and L. Rei (2019) How effective is machine learning to detect long transient gravitational waves from neutron stars in a real search?. arXiv e-prints, pp. arXiv:1909.02262. External Links: 1909.02262 Cited by: Introduction..
  • F. Morawski, M. Bejger, and P. Ciecieląg (2019) Deep learning classification of the continuous gravitational-wave signal candidates from the time-domain f-statistic search. arXiv:1907.06917. Cited by: Introduction..
  • A. Mytidis, A. A. Panagopoulos, O. P. Panagopoulos, A. Miller, and B. Whiting (2019) Sensitivity study using machine learning algorithms on simulated -mode gravitational wave signals from newborn neutron stars. Phys. Rev. D 99, pp. 024024. External Links: Document, Link Cited by: Introduction..
  • H. Nakano, T. Narikawa, K. Oohara, K. Sakai, H. Shinkai, H. Takahashi, T. Tanaka, N. Uchikata, S. Yamamoto, and T. S. Yamamoto (2019) Comparison of various methods to extract ringdown frequency from gravitational wave data. Phys. Rev. D 99, pp. 124032. External Links: Document, Link Cited by: Introduction..
  • Y. Pan, A. Buonanno, A. Taracchini, L. E. Kidder, A. H. Mroué, H. P. Pfeiffer, M. A. Scheel, and B. Szilágyi (2014) Inspiral-merger-ringdown waveforms of spinning, precessing black-hole binaries in the effective-one-body formalism. Phys. Rev. D 89, pp. 084006. External Links: Document, Link Cited by: Introduction..
  • D. Pollard (2002) A user’s guide to measure theoretic probability. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press. External Links: ISBN 9780521002899, LCCN 2001035270, Link Cited by: Training neural networks to produce posteriors..
  • A. Rebei, E. A. Huerta, S. Wang, S. Habib, R. Haas, D. Johnson, and D. George (2019) Fusing numerical relativity and deep learning to detect higher-order multipole waveforms from eccentric binary black hole mergers. Phys. Rev. D 100, pp. 044025. External Links: Document, Link Cited by: Introduction..
  • D. W. Ruck, S. K. Rogers, M. Kabrisky, M. E. Oxley, and B. W. Suter (1990) The multilayer perceptron as an approximation to a bayes optimal discriminant function. IEEE Transactions on Neural Networks 1 (4), pp. 296–298. Cited by: Training neural networks to produce posteriors..
  • H. Shen, E. Huerta, and Z. Zhao (2019) Deep learning at scale for gravitational wave parameter estimation of binary black hole mergers. arXiv:1903.01998. Cited by: Introduction..
  • F. Tonolini, A. Lyons, P. Caramazza, D. Faccio, and R. Murray-Smith (2019) Variational inference for computational imaging inverse problems. arXiv preprint arXiv:1904.06264. Cited by: Introduction..
  • S. A. Usman, A. H. Nitz, I. W. Harry, C. M. Biwer, D. A. Brown, M. Cabero, C. D. Capano, T. D. Canton, T. Dent, S. Fairhurst, et al. (2016) The PyCBC search for gravitational waves from compact binary coalescence. Classical and Quantum Gravity 33 (21), pp. 215004. External Links: Document, Link Cited by: Introduction..
  • M. Vallisneri (2008) Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects. Phys. Rev. D 77, pp. 042001. External Links: Document, Link Cited by: Introduction..
  • E. A. Wan (1990) Neural network classification: a bayesian interpretation. IEEE Transactions on Neural Networks 1 (4), pp. 303–305. Cited by: Training neural networks to produce posteriors..