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Complex Regression Modeling

Deeply Learned Generalized Linear Models with Missing Data

ORCID Icon, , &
Pages 638-650 | Received 05 Jul 2022, Accepted 17 Oct 2023, Published online: 15 Dec 2023

References

  • Beesley, L. J., Taylor, J. M., and Little, R. J. (2019), “Sequential Imputation for Models with Latent Variables Assuming Latent Ignorability,” Australian & New Zealand Journal of Statistics, 61, 213–233. DOI: 10.1111/anzs.12264.
  • Bottou, L. (2012), “Stochastic Gradient Descent Tricks,” in Neural Networks: Tricks of the Trade, eds. G. Montavon, G. B. Orr, and K.-R. Müller, pp. 421–436, Berlin: Springer.
  • Burda, Y., Grosse, R., and Salakhutdinov, R. (2015), “Importance Weighted Autoencoders,” arXiv e-prints p. arXiv:1509.00519.
  • Chen, D., Liu, S., Kingsbury, P., Sohn, S., Storlie, C. B., Habermann, E. B., Naessens, J. M., Larson, D. W., and Liu, H. (2019), “Deep Learning and Alternative Learning Strategies for Retrospective Real-World Clinical Data,” npj Digital Medicine, 2, 43. DOI: 10.1038/s41746-019-0122-0.
  • Cremer, C., Morris, Q., and Duvenaud, D. (2017), “Reinterpreting Importance-Weighted Autoencoders,” arXiv e-prints p. arXiv:1704.02916.
  • Diggle, P., and Kenward, M. G. (1994), “Informative Drop-Out in Longitudinal Data Analysis,” Applied Statistics, 43, 49–93. DOI: 10.2307/2986113.
  • Dormehl, L. (2019), “What is An Artificial Neural Network? Here’s Everything You Need to Know,” available at https://www.digitaltrends.com/cool-tech/what-is-an-artificial-neural-network/
  • Dua, D., and Graff, C. (2017), “UCI Machine Learning Repository,” available at http://archive.ics.uci.edu/ml.
  • Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
  • Gershman, S. J., and Goodman, N. D. (2014), “Amortized Inference in Probabilistic Reasoning,” in CogSci.
  • Ghorbani, A., and Zou, J. Y. (2018), “Embedding for Informative Missingness: Deep Learning with Incomplete Data,” in 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, pp. 437–445. DOI: 10.1109/ALLERTON.2018.8636008.
  • Guo, H., and Gelfand, S. B. (1990), “Analysis of Gradient Descent Learning Algorithms for Multilayer Feedforward Neural Networks,” in 29th IEEE Conference on Decision and Control, IEEE, pp. 1751–1756. DOI: 10.1109/CDC.1990.203921.
  • Hapfelmeier, A., Hothorn, T., Ulm, K., and Strobl, C. (2012), “A New Variable Importance Measure for Random Forests with Missing Data,” Statistics and Computing, 24, 21–34. DOI: 10.1007/s11222-012-9349-1.
  • Holland, P. W., and Welsch, R. E. (1977), “Robust Regression Using Iteratively Reweighted Least-Squares,” Communications in Statistics - Theory and Methods, 6, 813–827. DOI: 10.1080/03610927708827533.
  • Hoogland, J., Barreveld, M., Debray, T. P. A., Reitsma, J. B., Verstraelen, T. E., Dijkgraaf, M. G. W., and Zwinderman, A. H. (2020), “Handling Missing Predictor Values When Validating and Applying a Prediction Model to New Patients,” Statistics in Medicine, 39, 3591–3607. DOI: 10.1002/sim.8682.
  • Ibrahim, J. G., Chen, M.-H., Lipsitz, S. R., and Herring, A. H. (2005), “Missing-Data Methods for Generalized Linear Models,” Journal of the American Statistical Association, 100, 332–346. DOI: 10.1198/016214504000001844.
  • Ibrahim, J. G., and Molenberghs, G. (2009), “Missing Data Methods in Longitudinal Studies: A Review,” TEST, 18, 1–43. DOI: 10.1007/s11749-009-0138-x.
  • Ipsen, N. B., Mattei, P.-A., and Frellsen, J. (2021), “How to Deal with Missing Data in Supervised Deep Learning?” in International Conference on Learning Representations.
  • Kingma, D. P., and Ba, J. (2014), “Adam: A Method for Stochastic Optimization,” arXiv e-prints p. arXiv:1412.6980.
  • Kingma, D. P., and Welling, M. (2013), “Auto-Encoding Variational Bayes,” arXiv e-prints p. arXiv:1312.6114.
  • ———(2019), “An Introduction to Variational Autoencoders,” arXiv e-prints p. arXiv:1906.02691.
  • Li, Y., Akbar, S., and Oliva, J. (2020), “Acflow: Flow Models for Arbitrary Conditional Likelihoods,” in International Conference on Machine Learning, PMLR, pp. 5831–5841.
  • Lim, D. K., Rashid, N. U., Oliva, J. B., and Ibrahim, J. G. (2021), “Handling Non-ignorably Missing Features in Electronic Health Records Data Using Importance-Weighted Autoencoders,” arXiv e-prints p. arXiv:2101.07357.
  • Lipsitz, S. R., and Ibrahim, J. G. (1996), “A Conditional Model for Incomplete Covariates in Parametric Regression Models,” Biometrika, 83, 916–922. DOI: 10.1093/biomet/83.4.916.
  • Little, R. J. A., and Rubin, D. B. (2002), Statistical Analysis with Missing Data, Hoboken, NJ: Wiley.
  • Lopez, R., Regier, J., Cole, M. B., Jordan, M. I., and Yosef, N. (2018), “Deep Generative Modeling for Single-Cell Transcriptomics,” Nature Methods, 15, 1053–1058. DOI: 10.1038/s41592-018-0229-2.
  • Ma, C., and Zhang, C. (2021), “Identifiable Generative Models for Missing not at Random Data Imputation,” Advances in Neural Information Processing Systems, 34, 27645–27658.
  • Mattei, P.-A., and Frellsen, J. (2019), “MIWAE: Deep Generative Modelling and Imputation of Incomplete Data Sets,” in Proceedings of the 36th International Conference on Machine Learning, Vol. 97 of Proceedings of Machine Learning Research, eds. K. Chaudhuri and R. Salakhutdinov, pp. 4413–4423, PMLR, Long Beach, California, USA.
  • McCullagh, P., and Nelder, J. A. (2019), Generalized Linear Models, Boca Raton, FL: Routledge.
  • Moro, S., Cortez, P., and Rita, P. (2014), “A Data-Driven Approach to Predict the Success of Bank Telemarketing,” Decision Support Systems, 62, 22–31. DOI: 10.1016/j.dss.2014.03.001.
  • Murphy, J. (2016), An Overview of Convolutional Neural Network Architectures for Deep Learning, pp. 1–22, Plymouth, MA: Microway Inc.
  • Nelder, J. A., and Wedderburn, R. W. M. (1972), “Generalized Linear Models,” Journal of the Royal Statistical Society, Series A, 135, 370–384. DOI: 10.2307/2344614.
  • Prechelt, L. (1998), “Early Stopping-but When?” in Neural Networks: Tricks of the Trade, eds. G. Montavon, G. B. Orr, and K.-R. Müller, pp. 55–69, Berlin: Springer.
  • Qi, M., and Wu, Y. (2003), “Nonlinear Prediction of Exchange Rates with Monetary Fundamentals,” Journal of Empirical Finance, 10, 623–640. DOI: 10.1016/S0927-5398(03)00008-2.
  • Razzak, M. I., Naz, S., and Zaib, A. (2017), “Deep Larning for Medical Iage Processing: Overview, Challenges and the Future,” in Classification in BioApps: Automation of Decision Making, Lecture Notes in Computational Vision and Biomechanics, eds. N. Dey, A. S. Ashour, and S. Borra, pp. 323–350, Cham: Springer.
  • Rubin, D. B. (1976), “Inference and Missing Data,” Biometrika, 63, 581–592. DOI: 10.1093/biomet/63.3.581.
  • ———(2004), Multiple Imputation for Nonresponse in Surveys (Vol. 81), Hoboken, NJ: Wiley.
  • Saxe, A. M., Mcclelland, J. L., and Ganguli, S. (2014), “Exact Solutions to the Nonlinear Dynamics of Learning in Deep Linear Neural Network,” in International Conference on Learning Representations.
  • Strauss, R., and Oliva, J. B. (2021), “Arbitrary Conditional Distributions with Energy,” Advances in Neural Information Processing Systems, 34, 752–763.
  • ———(2022), “Posterior Matching for Arbitrary Conditioning,” in Advances in Neural Information Processing Systems (Vol. 35), pp. 18088–18099.
  • Stubbendick, A. L., and Ibrahim, J. G. (2003), “Maximum Likelihood Methods for Nonignorable Missing Responses and Covariates in Random Effects Models,” Biometrics, 59, 1140–1150. DOI: 10.1111/j.0006-341x.2003.00131.x.
  • Svozil, D., Kvasnicka, V., and Pospichal, J. (1997), “Introduction to Multi-Layer Feed-Forward Neural Networks,” Chemometrics and Intelligent Laboratory Systems, 39, 43–62. DOI: 10.1016/S0169-7439(97)00061-0.
  • Tran, M.-N., Nguyen, N., Nott, D., and Kohn, R. (2019), “Bayesian Deep Net GLM and GLMM,” Journal of Computational and Graphical Statistics, 29, 97–113. DOI: 10.1080/10618600.2019.1637747.
  • Van Buuren, S. (2018), Flexible Imputation of Missing Data, Boca Raton, FL: CRC Press.
  • Van Buuren, S., and Groothuis-Oudshoorn, K. (2011), “mice: Multivariate Imputation by Chained Equations in r,” Journal of Statistical Software, 45, 1–67. DOI: 10.18637/jss.v045.i03.
  • Wells, B. J., Nowacki, A. S., Chagin, K., and Kattan, M. W. (2013), “Strategies for Handling Missing Data in Electronic Health Record Derived Data,” eGEMs (Generating Evidence &: Methods to Improve Patient Outcomes), 1, 7. DOI: 10.13063/2327-9214.1035.

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