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Articles

Active Learning for Deep Gaussian Process Surrogates

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Pages 4-18 | Received 22 May 2021, Accepted 14 Sep 2021, Published online: 02 Feb 2022

References

  • Ba, S., and Joseph, V. R. (2012), “Composite Gaussian Process Models for Emulating Expensive Functions,” The Annals of Applied Statistics, 1838–1860. DOI: 10.1214/12-AOAS570.
  • Barnett, S. (1979), Matrix Methods for Engineers and Scientists, McGraw-Hill.
  • Berger, J. O., De Oliveira, V., and Sansó, B. (2001). “Objective Bayesian Analysis of Spatially Correlated Data,” Journal of the American Statistical Association, 96, 1361–1374. DOI: 10.1198/016214501753382282.
  • Binois, M., Huang, J., Gramacy, R. B., and Ludkovski, M. (2019), “Replication or Exploration? Sequential Design for Stochastic Simulation Experiments,” Technometrics, 61, 1, 7–23. DOI: 10.1080/00401706.2018.1469433.
  • Bornn, L., Shaddick, G., and Zidek, J. V. (2012), “Modeling Nonstationary Processes Through Dimension Expansion,” Journal of the American Statistical Association, 107, 281–289. DOI: 10.1080/01621459.2011.646919.
  • Bui, T., Hernández-Lobato, D., Hernandez-Lobato, J., Li, Y., and Turner, R. (2016), “Deep Gaussian Processes for Regression Using Approximate Expectation Propagation,” in International Conference on Machine Learning, 1472–1481. PMLR.
  • Cohn, D. (1994), “Neural Network Exploration Using Optimal Experiment Design,” in Advances in Neural Information Processing Systems (Vol. 6), 679–686, Morgan-Kaurmann.
  • Cole, D. A., Christianson, R. B., and Gramacy, R. B. (2021), “Locally Induced Gaussian Processes for Large-Scale Simulation Experiments,” Statistics and Computing, 31, 3, 1–21. DOI: 10.1007/s11222-021-10007-9.
  • Cutajar, K., Pullin, M., Damianou, A., Lawrence, N., and González, J. (2019), “Deep Gaussian Processes for Multi-Fidelity Modeling,” arXiv:1903.07320.
  • Damianou, A., and Lawrence, N. D. (2013), “Deep Gaussian Processes,” in Artificial Intelligence and Statistics, PMLR, pp. 207–215.
  • Deissenberg, C., Van Der Hoog, S., and Dawid, H. (2009), “EURACE: A Massively Parallel Agent-Based Model of the European Economy,” Applied Mathematics and Computation, 204, 2, 541–552. DOI: 10.1016/j.amc.2008.05.116.
  • Dunlop, M. M., Girolami, M. A., Stuart, A. M., and Teckentrup, A. L. (2018), “How Deep Are Deep Gaussian Processes?” Journal of Machine Learning Research, 19, 1–46.
  • Dutordoir, V., Knudde, N., van der Herten, J., Couckuyt, I., and Dhaene, T. (2017), “Deep Gaussian Process Metamodeling of Sequentially Sampled Non-Stationary Response Surfaces,” in 2017 Winter Simulation Conference (WSC), IEEE, pp. 1728–1739. DOI: 10.1109/WSC.2017.8247911.
  • Duvenaud, D., Rippel, O., Adams, R., and Ghahramani, Z. (2014), “Avoiding Pathologies in Very Deep Networks,” in Artificial Intelligence and Statistics, PMLR, pp. 202–210.
  • Fadikar, A., Higdon, D., Chen, J., Lewis, B., Venkatramanan, S., and Marathe, M. (2018), “Calibrating a Stochastic, Agent-based Model Using Quantile-Based Emulation,” SIAM/ASA Journal on Uncertainty Quantification, 6, 1685–1706. DOI: 10.1137/17M1161233.
  • Fei, J., Zhao, J., Sun, S., and Liu, Y. (2018), “Active Learning Methods With Deep Gaussian Processes.” in International Conference on Neural Information Processing, 473–483. Springer, pp. 473–483.
  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013), Bayesian Data Analysis, New York: CRC Press.
  • Gneiting, T. and Raftery, A. E. (2007). “Strictly Proper Scoring Rules, Prediction, and Estimation,” Journal of the American Statistical Association, 102, 359–378. DOI: 10.1198/016214506000001437.
  • Gramacy, R. B. (2007), “tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models,” Journal of Statistical Software, 19, 1–46. DOI: 10.18637/jss.v019.i09.
  • Gramacy, R. B. (2016), “laGP: Large-Scale Spatial Modeling via Local Approximate Gaussian Processes in R,” Journal of Statistical Software, 72, 1, 1–46.
  • Gramacy, R. B. (2020), Surrogates: Gaussian Process Modeling, Design and Optimization for the Applied Sciences, Boca Raton, FL: Chapman Hall/CRC.
  • Gramacy, R. B., and Apley, D. W. (2015), “Local Gaussian Process Approximation for Large Computer Experiments,” Journal of Computational and Graphical Statistics, 24, 561–578. DOI: 10.1080/10618600.2014.914442.
  • Gramacy, R. B., and Lee, H. K. H. (2008), “Bayesian Treed Gaussian Process Models With an Application to Computer Modeling,” Journal of the American Statistical Association, 103, 1119–1130. DOI: 10.1198/016214508000000689.
  • Gramacy, R. B., and Lee, H. K. H. (2009), “Adaptive Design and Analysis of Supercomputer Experiments,” Technometrics, 51, 130–145.
  • Havasi, M., Hernández-Lobato, J. M., and Murillo-Fuentes, J. J. (2018), “Inference in Deep Gaussian Processes Using Stochastic Gradient Hamiltonian Monte Carlo,” in Advances in Neural Information Processing Systems, pp. 7506–7516.
  • Hebbal, A., Brevault, L., Balesdent, M., Talbi, E.-G., and Melab, N. (2021). “Bayesian Optimization Using Deep Gaussian Processes With Applications to Aerospace System Design,” Optimization and Engineering, 22, 321–361. DOI: 10.1007/s11081-020-09517-8.
  • Higdon, D., Kennedy, M., Cavendish, J. C., Cafeo, J. A., and Ryne, R. D. (2004), “Combining Field Data and Computer Simulations for Calibration and Prediction,” SIAM Journal on Scientific Computing, 26, 448–466. DOI: 10.1137/S1064827503426693.
  • Higdon, D., Swall, J., and Kern, J. (1999), “Non-Stationary Spatial Modeling,” Bayesian Statistics, 6, 761–768.
  • Higdon, D. M., Lee, H., and Holloman, C. (2003), “Markov chain Monte Carlo-Based Approaches for Inference in Computationally Intensive Inverse Problems” (with discussion), in Bayesian Statistics 7. Proceedings of the Seventh Valencia International Meeting, eds. J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith, and M. West, Oxford: Oxford University Press, pp. 181–197.
  • Johnson, M. E., Moore, L. M., and Ylvisaker, D. (1990), “Minimax and Maximin Distance Designs,” Journal of Statistical Planning and Inference, 26, 131–148. DOI: 10.1016/0378-3758(90)90122-B.
  • Jones, D. R., Schonlau, M., and Welch, W. J. (1998), “Efficient Global Optimization of Expensive Black-Box Functions,” Journal of Global Optimization, 13, 455–492. DOI: 10.1023/A:1008306431147.
  • Joseph, V. R., Gu, L., Ba, S., and Myers, W. R. (2019), “Space-Filling Designs for Robustness Experiments,” Technometrics, 61, 24–37. DOI: 10.1080/00401706.2018.1451390.
  • Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. M. (1998). “Markov Chain Monte Carlo in Practice: A Roundtable Discussion,” The American Statistician, 52, 93–100.
  • Katzfuss, M. (2013), “Bayesian Nonstationary Spatial Modeling for Very Large Datasets,” Environmetrics, 24, 189–200. DOI: 10.1002/env.2200.
  • Kennedy, M. C., and O’Hagan, A. (2001). “Bayesian Calibration of Computer Models,” Journal of the Royal Statistical Society, Series B, 63, 425–464. DOI: 10.1111/1467-9868.00294.
  • MacKay, D. J. (1992). “Information-Based Objective Functions for Active Data Selection,” Neural Computation, 4, 590–604. DOI: 10.1162/neco.1992.4.4.590.
  • Marmin, S., and Filippone, M. (2018), “Variational Calibration of Computer Models,” arXiv:1810.12177.
  • Marrel, A., Iooss, B., Laurent, B., and Roustant, O. (2009), “Calculations of Sobol Indices for the Gaussian Process Metamodel,” Reliability Engineering & System Safety, 94, 742–751.
  • McKay, M. D., Beckman, R. J., and Conover, W. J. (2000), “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,” Technometrics, 42, 55– 61. DOI: 10.1080/00401706.2000.10485979.
  • Mehta, P. M., Walker, A., Lawrence, E., Linares, R., Higdon, D., and Koller, J. (2014), “Modeling Satellite Drag Coefficients With Response Surfaces,” Advances in Space Research, 54, 1590–1607. DOI: 10.1016/j.asr.2014.06.033.
  • Microsoft and Weston, S. (2020), foreach: Provides Foreach Looping Construct, R package version 1.5.0.
  • Morris, M. D., and Mitchell, T. J. (1995), “Exploratory Designs for Computational Experiments,” Journal of Statistical Planning and Inference, 43, 381–402. DOI: 10.1016/0378-3758(94)00035-T.
  • Murray, I., Adams, R. P., and MacKay, D. J. C. (2010), “Elliptical slice sampling.” In The Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, Vol. 9 of JMLR: W&CP. PMLR, pp. 541–548.
  • Neal, R. M. (2011). “MCMC Using Hamiltonian Dynamics,” in Handbook of Markov Chain Monte Carlo (Vol. 2), p. 2.
  • Oakley, J. E., and O’Hagan, A. (2004), “Probabilistic Sensitivity Analysis of Complex Models: A Bayesian Approach,” Journal of the Royal Statistical Society, Series B, 66, 751–769. DOI: 10.1111/j.1467-9868.2004.05304.x.
  • Oliver, D. S., Cunha, L. B., and Reynolds, A. C. (1997), “Markov Chain Monte Carlo Methods for Conditioning a Permeability Field to Pressure Data,” Mathematical Geology, 29, 61–91. DOI: 10.1007/BF02769620.
  • Paciorek, C. J., and Schervish, M. J. (2003). “Nonstationary Covariance Functions for Gaussian Process Regression,” in Proceedings of the 16th International Conference on Neural Information Processing Systems (NIPS’03), Cambridge, MA: MIT Press, pp. 273–280.
  • Picheny, V., Gramacy, R., Wild, S., and Le Digabel, S. (2016), “Bayesian Optimization Under Mixed Constraints With a Slack-Variable Augmented Lagrangian,” in Advances in Neural Information Processing Systems, pp. 1435–1443.
  • Radaideh, M. I., and Kozlowski, T. (2020), “Surrogate Modeling of Advanced Computer Simulations Using Deep Gaussian Processes,” Reliability Engineering & System Safety, 195, 106731.
  • Rajaram, D., Puranik, T. G., Ashwin Renganathan, S., Sung, W., Fischer, O. P., Mavris, D. N., and Ramamurthy, A. (2021), “Empirical Assessment of Deep Gaussian Process Surrogate Models for Engineering Problems,” Journal of Aircraft, 58, 1, 182–196. DOI: 10.2514/1.C036026.
  • Rasmussen, C. E. (2000), “The Infinite Gaussian Mixture Model,” in Advances in Neural Information Processing Systems (vol. 12). MIT Press, pp. 554–560.
  • Rasmussen, C. E., and Ghahramani, Z. (2002), “Infinite Mixtures of Gaussian Process Experts,” in Advances in Neural Information Processing Systems (vol. 2), Cambridge, MA: MIT, pp. 881–888.
  • Rasmussen, C. E., and Williams, C. K. I. (2005), Gaussian Processes for Machine Learning, Cambridge, MA: MIT Press.
  • Salimbeni, H., and Deisenroth, M. (2017), “Doubly Stochastic Variational Inference for Deep Gaussian Processes,” arXiv:1705.08933.
  • Saltelli, A. (2002). “Making Best Use of Model Evaluations to Compute Sensitivity Indices,” Computer Physics Communications, 145, 280–297. DOI: 10.1016/S0010-4655(02)00280-1.
  • Sampson, P. D., and Guttorp, P. (1992), “Nonparametric Estimation of Nonstationary Spatial Covariance Structure,” Journal of the American Statistical Association, 87, 108–119. DOI: 10.1080/01621459.1992.10475181.
  • Santner, T., Williams, B., and Notz, W. (2018), The Design and Analysis of Computer Experiments (2nd ed.), New York: Springer–Verlag.
  • Sauer, A. (2020), deepgp: Sequential Design for Deep Gaussian Processes Using MCMC, R package version 0.1.0.
  • Schmidt, A. M., and O’Hagan, A. (2003). “Bayesian Inference for Non-Stationary Spatial Covariance Structure Via Spatial Deformations,” Journal of the Royal Statistical Society, Series B, 65, 743–758. DOI: 10.1111/1467-9868.00413.
  • Sejdinovic, D., Strathmann, H., Garcia, M. L., Andrieu, C., and Gretton, A. (2014). “Kernel Adaptive Metropolis–Hastings,” in International Conference on Machine Learning, pp. 1665–1673. PMLR.
  • Seo, S., Wallat, M., Graepel, T., and Obermayer, K. (2000), “Gaussian Process Regression: Active Data Selection and Test Point Rejection,” in Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks, vol. 3. IEEE, pp. 241–246.
  • Shewry, M. C. and Wynn, H. P. (1987), “Maximum Entropy Sampling,” Journal of Applied Statistics, 14, 165–170. DOI: 10.1080/02664768700000020.
  • Snoek, J., Larochelle, H., and Adams, R. P. (2012), “Practical Bayesian Optimization of Machine Learning Algorithms,” in Advances in Neural Information Processing Systems (vol. 25). Curran Associates, Inc., pp. 2951–2959.
  • Stein, M. L. (1999), Interpolation of Spatial Data, Springer-Verlag.
  • Sun, F., Gramacy, R. B., Haaland, B., Lawrence, E., and Walker, A. (2019), “Emulating Satellite Drag From Large Simulation Experiments,” SIAM/ASA Journal on Uncertainty Quantification, 7, 720–759. DOI: 10.1137/18M1170157.
  • Wang, Y., Brubaker, M., Chaib-Draa, B., and Urtasun, R. (2016). “Sequential Inference for Deep Gaussian Process,” in Artificial Intelligence and Statistics, PMLR, pp. 694–703.
  • Yang, J. and Klabjan, D. (2020), “Bayesian Active Learning for Choice Models With Deep Gaussian Processes,” IEEE Transactions on Intelligent Transportation Systems, 22, 1080–1092. DOI: 10.1109/TITS.2019.2962535.
  • Zhang, B., Cole, D. A., and Gramacy, R. B. (2021), “Distance-Distributed Design for Gaussian Process Surrogates,” Technometrics, 63, 40–52. DOI: 10.1080/00401706.2019.1677269.

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