Main Effects and Interactions in Mixed and Incomplete Data Frames

References

• Agarwal, D., Zhang, L., and Mazumder, R. (2011), “Modeling Item–Item Similarities for Personalized Recommendations on Yahoo! Front Page,” The Annals of Applied Statistics, 5, 1839–1875. DOI: 10.1214/11-AOAS475.
   Web of Science ®Google Scholar
• Agresti, A. (2013), Categorical Data Analysis (3rd ed.), Hoboken, NJ: Wiley.
   Google Scholar
• Bühlmann, P., and van de Geer, S. (2011), Statistics for High-Dimensional Data: Methods, Theory and Applications, Berlin, Heidelberg: Springer.
   Google Scholar
• Cai, T., and Zhou, W.-X. (2013), “A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion,” Journal of Machine Learning Research, 14, 3619–3647.
   Web of Science ®Google Scholar
• Candès, E. J., Li, X., Ma, Y., and Wright, J. (2011), “Robust Principal Component Analysis?,” Journal of the ACM, 58, 11. DOI: 10.1145/1970392.1970395.
   Web of Science ®Google Scholar
• Cao, Y., and Xie, Y. (2016), “Poisson Matrix Recovery and Completion,” IEEE Transactions on Signal Processing, 64, 1609–1620. DOI: 10.1109/TSP.2015.2500192.
   Web of Science ®Google Scholar
• Chandrasekaran, V., Sanghavi, S., Parrilo, P. A., and Willsky, A. S. (2011), “Rank-Sparsity Incoherence for Matrix Decomposition,” SIAM Journal on Optimization, 21, 572–596. DOI: 10.1137/090761793.
   Web of Science ®Google Scholar
• Davenport, M. A., Plan, Y., van den Berg, E., and Wootters, M. (2012), “1-Bit Matrix Completion,” CoRR, arXiv no. 1209.3672.
   Google Scholar
• Fithian, W., and Mazumder, R. (2018), “Flexible Low-Rank Statistical Modeling With Missing Data and Side Information,” Statistical Science, 33, 238–260. DOI: 10.1214/18-STS642.
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1. DOI: 10.18637/jss.v033.i01.
   PubMed Web of Science ®Google Scholar
• Gelman, A., and Hill, J. (2007), Data Analysis Using Regression and Multilevel/Hierarchical Models, New York: Cambridge University Press.
   Google Scholar
• Gunasekar, S., Ravikumar, P., and Ghosh, J. (2014), “Exponential Family Matrix Completion Under Structural Constraints,” in Proceedings of the 31st International Conference on International Conference on Machine Learning, ICML’14 (Vol. 32), JMLR.org, pp. II-1917–II-1925.
   Google Scholar
• Hastie, T., Mazumder, R., Lee, J., and Zadeh, R. (2015), “Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares,” The Journal of Machine Learning Research, 16, 3367–3402.
   PubMed Web of Science ®Google Scholar
• Heeringa, S., West, B., and Berlung, P. (2010), Applied Survey Data Analysis, New York: Chapman and Hall/CRC.
   Google Scholar
• Hsu, D., Kakade, S. M., and Zhang, T. (2011), “Robust Matrix Decomposition With Sparse Corruptions,” EEE Transactions on Information Theory, 57, 7221–7234. DOI: 10.1109/TIT.2011.2158250.
   Web of Science ®Google Scholar
• Husson, F., Josse, J., Narasimhan, B., and Robin, G. (2018), “Imputation of Mixed Data With Multilevel Singular Value Decomposition,” arXiv no. 1804.11087. DOI: 10.1080/10618600.2019.1585261.
   Google Scholar
• Josse, J., and Husson, F. (2016), “missMDA: A Package for Handling Missing Values in Multivariate Data Analysis,” Journal of Statistical Software, 70, 1–31. DOI: 10.18637/jss.v070.i01.
   Web of Science ®Google Scholar
• Kiers, H. A. L. (1991), “Simple Structure in Component Analysis Techniques for Mixtures of Qualitative and Quantitative Variables,” Psychometrika, 56, 197–212. DOI: 10.1007/BF02294458.
   Web of Science ®Google Scholar
• Klopp, O., Lafond, J., Moulines, É., and Salmon, J. (2015), “Adaptive Multinomial Matrix Completion,” Electronic Journal of Statistics, 9, 2950–2975. DOI: 10.1214/15-EJS1093.
   Web of Science ®Google Scholar
• Klopp, O., Lounici, K., and Tsybakov, A. B. (2017), “Robust Matrix Completion,” Probability Theory and Related Fields, 169, 523–564. DOI: 10.1007/s00440-016-0736-y.
   Web of Science ®Google Scholar
• Kumar, N. K., and Schneider, J. (2017), “Literature Survey on Low Rank Approximation of Matrices,” Linear and Multilinear Algebra, 65, 2212–2244. DOI: 10.1080/03081087.2016.1267104.
   Web of Science ®Google Scholar
• Lafond, J. (2015), “Low Rank Matrix Completion With Exponential Family Noise,” Journal of Machine Learning Research: Workshop and Conference Proceedings, 40, 1–18.
   Google Scholar
• Landgraf, A. J., and Lee, Y. (2015), “Generalized Principal Component Analysis: Projection of Saturated Model Parameters,” Technical Report, The Ohio State University, Department of Statistics.
   Google Scholar
• Legendre, P., Galzin, R., and Harmelin-Vivien, M. L. (1997), “Relating Behavior to Habitat: Solutions to the Fourth-Corner Problem,” Ecology, 78, 547–562. DOI: 10.2307/2266029.
   Web of Science ®Google Scholar
• Little, R. J. A., and Rubin, D. B. (2002), Statistical Analysis With Missing Data, Wiley Series in Probability and Statistics, New York: Wiley.
   Google Scholar
• Mao, X., Chen, S. X., and Wong, R. K. W. (2019), “Matrix Completion With Covariate Information,” Journal of the American Statistical Association, 114, 198–210. DOI: 10.1080/01621459.2017.1389740.
   Web of Science ®Google Scholar
• Mardani, M., Mateos, G., and Giannakis, G. B. (2013), “Recovery of Low-Rank Plus Compressed Sparse Matrices With Application to Unveiling Traffic Anomalies,” IEEE Transactions on Information Theory, 59, 5186–5205. DOI: 10.1109/TIT.2013.2257913.
   Web of Science ®Google Scholar
• Mazumder, R., Hastie, T., and Tibshirani, R. (2010), “Spectral Regularization Algorithms for Learning Large Incomplete Matrices,” The Journal of Machine Learning Research, 11, 2287–2322.
   PubMed Web of Science ®Google Scholar
• Murdoch, T., and Detsky, A. (2013), “The Inevitable Application of Big Data to Health Care,” JAMA, 309, 1351–1352. DOI: 10.1001/jama.2013.393.
   PubMed Web of Science ®Google Scholar
• Pagès, J. (2015), Multiple Factor Analysis by Example Using R, The R Series Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• R Core Team (2017), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Srebro, N., and Jaakkola, T. (2003), “Weighted Low-Rank Approximations,” in Proceedings of the Twentieth International Conference on International Conference on Machine Learning, ICML’03, AAAI Press, pp. 720–727.
   Google Scholar
• ter Braak, C. J., Peres-Neto, P., and Dray, S. (2017), “A Critical Issue in Model-Based Inference for Studying Trait-Based Community Assembly and a Solution,” PeerJ, 5, e2885. DOI: 10.7717/peerj.2885.
   PubMed Web of Science ®Google Scholar
• Tseng, P., and Yun, S. (2009), “A Coordinate Gradient Descent Method for Nonsmooth Separable Minimization,” Mathematical Programming, 117, 387–423. DOI: 10.1007/s10107-007-0170-0.
   Web of Science ®Google Scholar
• Tsybakov, A. B. (2008), Introduction to Nonparametric Estimation (1st ed.), New York: Springer Publishing Company, Inc.
   Google Scholar
• Udell, M., Horn, C., Zadeh, R., and Boyd, S. (2016), “Generalized Low Rank Models,” Foundations and Trends in Machine Learning, 9, 1–118. DOI: 10.1561/2200000055.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Xu, H., Caramanis, C., and Sanghavi, S. (2010), “Robust PCA via Outlier Pursuit,” in Proceedings of the 23rd International Conference on Neural Information Processing Systems, NIPS’10, USA, Curran Associates Inc., pp. 2496–2504.
   Google Scholar