The frontier of simulation-based inference

[en] Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the rapidly developing field of simulation-based inference and identify the forces giving new momentum to the field. Finally, we describe how the frontier is expanding so that a broad audience can appreciate the profound change these developments may have on science.

Disciplines :

Physics
Computer science

Author, co-author :

Cranmer, Kyle

Brehmer, Johann

Louppe, Gilles ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Big Data

Language :

English

Title :

The frontier of simulation-based inference

Publication date :

29 May 2020

Journal title :

Proceedings of the National Academy of Sciences of the United States of America

ISSN :

0027-8424

eISSN :

1091-6490

Publisher :

National Academy of Sciences, Washington DC, United States - District of Columbia

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 25 November 2019

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Scopus citations^®

302

Scopus citations^®
without self-citations

290

OpenCitations

141

Bibliography

P. J. Diggle, R. J. Gratton, Monte Carlo methods of inference for implicit statistical models. J. R. Stat. Soc. Ser. B 46, 193–212 (1984).
D. B. Rubin, Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Stat. 12, 1151–1172 (1984).
M. A. Beaumont, W. Zhang, D. J. Balding, Approximate Bayesian computation in population genetics. Genetics 162, 2025–2035 (2002).
S. Mohamed, B. Lakshminarayanan, Learning in implicit generative models. arXiv:1610.03483 (11 October 2016).
S. A. Sisson, Y. Fan, M. Beaumont, Handbook of Approximate Bayesian Computation (Chapman and Hall/CRC, 2018).
P. Marjoram, J. Molitor, V. Plagnol, S. Tavaré, Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U.S.A. 100, 15324–15328 (2003).
S. A. Sisson, Y. Fan, M. M. Tanaka, Sequential Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U.S.A. 104, 1760–1765 (2007).
G. W. Peters, Y. Fan, S. A. Sisson, On sequential Monte Carlo, partial rejection control and approximate Bayesian computation. Stat. Comput. 22, 1209–1222 (2012).
J. Brehmer, K. Cranmer, G. Louppe, J. Pavez, A guide to constraining effective field theories with machine learning. Phys. Rev. D 98, 052004 (2018).
Y. LeCun, Y. Bengio, G. Hinton, Deep learning. Nature 521, 436–444 (2015).
L. Dinh, D. Krueger, Y. Bengio, NICE: Non-linear independent components estimation. arXiv:1410.8516 (30 October 2014).
L. Dinh, J. Sohl-Dickstein, S. Bengio, “Density estimation using real NVP” in 5th International Conference on Learning Representations, ICLR 2017. April 24-26, 2017, Conference Track Proceedings (Toulon, France, 2017).
D. P. Kingma, P. Dhariwal, “Glow: Generative flow with invertible 1×1 convolutions” in Advances in Neural Information Processing Systems 2018 (2018), pp. 10215–10224.
M. Germain, K. Gregor, I. Murray, H. Larochelle, “MADE: Masked autoencoder for distribution estimation” in 32nd International Conference on Machine Learning, ICML 2015, vol. 2, pp. 881–889.
B. Uria, M. A. Côté, K. Gregor, I. Murray, H. Larochelle, Neural autoregressive distribution estimation. J. Mach. Learn. Res. 17, 7184–7220 (2016).
A. Van Den Oord, N. Kalchbrenner, K. Kavukcuoglu, “Pixel recurrent neural networks” in 33rd International Conference on Machine Learning, ICML 2016 (2016), vol. 4, pp. 2611–2620.
A. Van Den Oord et al., “Conditional image generation with PixelCNN decoders” in Advances in Neural Information Processing Systems (2016), pp. 4797–4805.
A. van den Oord et al., WaveNet: A generative model for raw audio. arXiv:1609.03499 (12 September 2016).
D. P. Kingma et al., Improving variational inference with inverse autoregressive flow. arXiv:1606.04934 (15 June 2016).
G. Papamakarios, T. Pavlakou, I. Murray, “Masked autoregressive flow for density estimation” in Advances in Neural Information Processing Systems 2017-December (2017), pp. 2339–2348.
C. W. Huang, D. Krueger, A. Lacoste, A. Courville, “Neural autoregressive flows” in 35th International Conference on Machine Learning, ICML 2018 (2018), vol. 5, pp. 3309–3324.
A. Wehenkel, G. Louppe, Unconstrained monotonic neural networks. arXiv:1908. 05164 (14 August 2019).
C. Durkan, A. Bekasov, I. Murray, G. Papamakarios, Cubic-spline flows. arXiv:1906. 02145 (5 June 2019).
C. Durkan, A. Bekasov, I. Murray., G. Papamakarios, Neural spline flows. arXiv:1906. 04032 (10 June 2019).
M. A. Hjortsø, P. Wolenski, “Neural ordinary differential equations” in Linear Mathematical Models in Chemical Engineering abs/1806 (2018), pp. 123–145.
W. Grathwohl, R. T. Q. Chen, J. Bettencourt, D. Duvenaud, Scalable reversible generative models with free-form continuous dynamics” in International Conference on Learning Representations (2019).
E. Meeds, M. Welling, “Gps-abc: Gaussian process surrogate approximate Bayesian computation” in Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence, UAI’14 (AUAI Press, Arlington, VA, 2014), pp. 593–602.
M. U. Gutmann, J. Corander, Bayesian optimization for likelihood-free inference of simulator-based statistical models. J. Mach. Learn. Res. 17, 4256–4302 (2016).
E. Meeds, M. Welling, “Optimization Monte Carlo: Efficient and embarrassingly parallel likelihood-free inference” in Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 2, NIPS’15 (MIT Press, Cambridge, MA, 2015), pp. 2080–2088.
M. Järvenpää, M. U. Gutmann, A. Pleska, A. Vehtari, P. Marttinen, Efficient acquisition rules for model-based approximate Bayesian computation. arXiv:1704.00520 (3 April 2017).
H. Wang, J. Li, Adaptive Gaussian process approximation for Bayesian inference with expensive likelihood functions. arXiv:1703.09930 (29 March 2017).
J. M. Lueckmann et al., “Flexible statistical inference for mechanistic models of neural dynamics” in Advances in Neural Information Processing Systems 2017-December (2017), pp. 1290–1300.
G. Papamakarios, D. C. Sterratt, I. Murray, “Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows” in International Conference on Artificial Intelligence and Statistics (2019).
P. Ranjan, D. Bingham, G. Michailidis, Sequential experiment design for contour estimation from complex computer codes. Technometrics 50, 527–541 (2008).
J. Bect, D. Ginsbourger, L. Li, V. Picheny, E. Vazquez, Sequential design of computer experiments for the estimation of a probability of failure. Stat. Comput. 22, 773–793 (2012).
L. Heinrich, G. Louppe, K. Cranmer, excursion (doi:10.5281/zenodo.1634428) (2018).
M. Cutler, T. J. Walsh, J. P. How, “Reinforcement learning with multi-fidelity simulators” in 2014 IEEE International Conference on Robotics and Automation (ICRA) (2014), pp. 3888–3895.
J. B. Hamrick et al., Metacontrol for adaptive imagination-based optimization. arXiv:1705.02670 (7 May 2017).
K. Kandasamy, G. Dasarathy, J. Schneider, B. Poczos, “Multi-fidelity Bayesian optimisation with continuous approximations” in Proceedings of the 34th International Conference on Machine Learning (JMLR. org, 2017), vol. 70, pp. 1799–1808.
A. D. Gordon, T. A. Henzinger, A. V. Nori, S. K. Rajamani, “Probabilistic programming” in Proceedings of the Conference on the Future of Software Engineering (ACM, New York, NY, 2014).
A. Doucet, A. M. Johansen, “A tutorial on particle filtering and smoothing: Fifteen years later” in Handbook of Nonlinear Filtering (2009), vol. 12, p. 3.
A. G. Baydin et al., Etalumis: Bringing probabilistic programming to scientific simulators at scale. arXiv:1907.03382 (8 July 2019).
M. M. Graham, A. J. Storkey, Asymptotically exact inference in differentiable generative models. Electron. J. Stat. 11, 5105–5164 (2017).
J. Brehmer, G. Louppe, J. Pavez, K. Cranmer, Mining gold from implicit models to improve likelihood-free inference. Proc. Natl. Acad. Sci. U.S.A. 117, 5242–5249 (2018).
M. Stoye, J. Brehmer, G. Louppe, J. Pavez, K. Cranmer, Likelihood-free inference with an improved cross-entropy estimator. arXiv:1808.00973 (2 August 2018).
A. G. Baydin, B. A. Pearlmutter, A. A. Radul, J. M. Siskind, Automatic differentiation in machine learning: A survey. J. Mach. Learn. Res. 18, 1–43 (2018).
C. Olah, Neural networks, types, and functional programming (2015). https://www.facebook.com/yann.lecun/posts/10155003011462143. Accessed 1 January 2018.
Y. LeCun, Deep learning est mort. vive differentiable programming! (2018). https://colah.github.io/posts/2015-09-NN-Types-FP/. Accessed 1 January 2018.
T. A. Le, A. G. Baydin, F. Wood, “Inference compilation and universal probabilistic programming” in Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017 (PMLR, Fort Lauderdale, FL, 2017), vol. 54, pp. 1338–1348.
D. J. Rezende, S. Mohamed, “Variational inference with normalizing flows” in 32nd International Conference on Machine Learning, ICML 2015 (2015), vol. 2, pp. 1530–1538.
G. Papamakarios, I. Murray, “Fast e-free inference of simulation models with Bayesian conditional density estimation” in Advances in Neural Information Processing Systems (2016), pp. 1036–1044.
R. Izbicki, A. B. Lee, T. Pospisil, ABC–CDE: Toward approximate Bayesian computation with complex high-dimensional data and limited simulations. J. Comput. Graph Stat. 28, 481–492 (2019).
B. Paige, F. Wood, “Inference networks for sequential Monte Carlo in graphical models” in 33rd International Conference on Machine Learning, ICML 2016 (2016), vol. 6, pp. 4434–4444.
D. Tran, R. Ranganath, D. M. Blei, “Hierarchical implicit models and likelihood-free variational inference” in Advances in Neural Information Processing Systems, I. Guyon et al., Eds. (2017), vol. 2017, pp. 5524–5534.
C. Durkan, G. Papamakarios, I. Murray, Sequential neural methods for likelihood-free inference. arXiv:1811.08723 (21 November 2018).
J. M. Lueckmann, G. Bassetto, T. Karaletsos, J. H. Macke, “Likelihood-free inference with emulator networks” in Proceedings of The 1st Symposium on Advances in Approximate Bayesian Inference, F. Ruiz, C. Zhang, D. Liang, T. Bui, Eds. (PMLR, 2019), vol. 96, pp. 32–53.
J. Alsing, T. Charnock, S. Feeney, B. Wandelt, Fast likelihood-free cosmology with neural density estimators and active learning. Mon. Not. R. Astron. Soc. 488, 4440–4458 (2019).
R. M. Neal, “Computing likelihood functions for high-energy physics experiments when distributions are defined by simulators with nuisance parameters” in Statistical Issues for LHC Physics. Proceedings, PHYSTAT-LHC 2007 (2007), pp. 111–118.
Y. Fan, D. J. Nott, S. A. Sisson, Approximate Bayesian computation via regression density estimation. Stat 2, 34–48 (2013).
K. Cranmer, J. Pavez, G. Louppe, Approximating likelihood ratios with calibrated discriminative classifiers. arXiv:1506.02169 (6 June 2015).
O. Thomas, R. Dutta, J. Corander, S. Kaski, M. U. Gutmann, Likelihood-free inference by ratio estimation. arXiv:1611.10242 (30 November 2016).
M. U. Gutmann, R. Dutta, S. Kaski, J. Corander, Likelihood-free inference via classification. Stat. Comput. 28, 411–425 (2018).
T. Dinev, M. U. Gutmann, Dynamic likelihood-free inference via ratio estimation (DIRE). arXiv:1810.09899 (23 October 2018).
J. Hermans, V. Begy, G. Louppe, Likelihood-free MCMC with approximate likelihood ratios. arXiv:1903.04057 (10 March 2019).
A. Andreassen, B. Nachman, Neural networks for full phase-space reweighting and parameter tuning. arXiv:1907.08209v1 (18 July 2019).
J. Brehmer, K. Cranmer, G. Louppe, J. Pavez, Constraining effective field theories with machine learning. Phys. Rev. Lett. 121, 111801 (2018).
G. Louppe, K. Cho, C. Becot, K. Cranmer, QCD-aware recursive neural networks for jet physics. JHEP 2019, 57 (2019).
A. Andreassen, I. Feige, C. Frye, M. D. Schwartz, JUNIPR: A framework for unsupervised machine learning in particle physics. Eur. Phys. J. C 79, 102 (2019).
G. Carleo et al., Machine learning and the physical sciences. Rev. Mod. Phys. 91, 045002 (2019).
A. Munk et al., Deep probabilistic surrogate networks for universal simulator approximation. arXiv:1910.11950 (25 October 2019).
J. Alsing, B. Wandelt, Generalized massive optimal data compression. Mon. Not. R. Astron. Soc. Lett. 476, L60–L64 (2018).
J. Alsing, B. Wandelt, S. Feeney, Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology. Mon. Not. R. Astron. Soc. 477, 2874–2885 (2018).
P. De Castro, T. Dorigo, INFERNO: Inference-aware neural optimisation. Comput. Phys. Commun. 244, 170–179 (2019).
J. Alsing, B. Wandelt, Nuisance hardened data compression for fast likelihood-free inference. Mon. Not. R. Astron. Soc. 488, 5093–5103 (2019).
S. S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9, 60–62 (1938).
A. Wald, Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Am. Math. Soc. 54, 426 (1943).
G. Cowan, K. Cranmer, E. Gross, O. Vitells, Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71, 1554 (2011).
F. Wood, J. W. Van De Meent, V. Mansinghka, A new approach to probabilistic programming inference J. Mach. Learn. Res. 33, 1024–1032 (2014).