Covariate-Adjusted Tensor Classification in High Dimensions

References

• Bach, F. R. (2008), “Consistency of the Group Lasso and Multiple Kernel Learning,” The Journal of Machine Learning Research, 9, 1179–1225.
   Web of Science ®Google Scholar
• Bao, Y. T., and Chien, J. T. (2015), “Tensor Classification Network,” in 2015 IEEE 25th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6, available at https://ieeexplore.ieee.org/.
   Google Scholar
• Becker, N., Werft, W., Toedt, G., Lichter, P., and Benner, A. (2009), “PenalizedSVM: A R-package for Feature Selection SVM Classification,” Bioinformatics, 25, 1711–1712.
   PubMed Web of Science ®Google Scholar
• Bellec, P., Chu, C., Chouinard-Decorte, F., Benhajali, Y., Margulies, D. S., and Craddock, R. C. (2017), “The Neuro Bureau ADHD-200 Preprocessed Repository,” NeuroImage, 144, 275–286.
   PubMed Web of Science ®Google Scholar
• Bickel, P., and Levina, E. (2004), “Some Theory for Fisher’s Linear Discriminant Function, ‘Naive Bayes’, and Some Alternatives When There are many More Variables than Observations,” Bernoulli, 10, 989–1010.
   Web of Science ®Google Scholar
• Bradley, P. S., and Mangasarian, O. L. (1998), “Feature Selection via Concave Minimization and Support Vector Machines,” in ICML (Vol. 98), pp. 82–90, available at http://proceedings.mlr.press/.
   Google Scholar
• Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32.
   Web of Science ®Google Scholar
• Cai, T., and Liu, W. (2011), “A Direct Estimation Approach to Sparse Linear Discriminant Analysis,” Journal of the American Statistical Association, 106, 1566–1577.
   Web of Science ®Google Scholar
• Chi, E. C., and Kolda, T. G. (2012), “On Tensors, Sparsity, and Nonnegative Factorizations,” SIAM Journal on Matrix Analysis and Applications, 33, 1272–1299.
   Web of Science ®Google Scholar
• Chiaromonte, F., Cook, R. D., and Li, B. (2002), “Sufficient Dimension Reduction in Regressions with Categorical Predictors,” The Annals of Statistics, 30, 475–497.
   Web of Science ®Google Scholar
• Clemmensen, L., Hastie, T., Witten, D., and Ersbøll, B. (2011), “Sparse Discriminant Analysis,” Technometrics, 53, 406–413.
   Web of Science ®Google Scholar
• Cook, R. D. (1998), Regression Graphics: Ideas for Studying Regressions Through Graphics (Vol. 318), New York: Wiley.
   Google Scholar
• Cortes, C., and Vapnik, V. (1995), “Support-Vector Networks,” Machine Learning, 20, 273–297.
   Web of Science ®Google Scholar
• Dimitriadou, E., Hornik, K., Leisch, F., Meyer, D., and Weingessel, A. (2009), “E1071: Misc Functions of the Department of Statistics (E1071), TU Wien,” CRAN R Package, R Foundation for Statistical Computing.
   Google Scholar
• Dutilleul, P. (1999), “The MLE Algorithm for the Matrix Normal Distribution,” Journal of Statistical Computation and Simulation, 64, 105–123.
   Web of Science ®Google Scholar
• Fan, J., and Fan, Y. (2008), “High Dimensional Classification using Features Annealed Independence Rules,” The Annals of Statistics, 36, 2605–2637.
   PubMed Web of Science ®Google Scholar
• Fan, J., Feng, Y., and Tong, X. (2012), “A Road to Classification in High Dimensional Space: The Regularized Optimal Affine Discriminant,” Journal of the Royal Statistical Society, Series B, 74, 745–771.
   Google Scholar
• Fan, J., Ke, Z. T., Liu, H., and Xia, L. (2015), “QUADRO: A Supervised Dimension Reduction method via Rayleigh Quotient Optimization,” The Annals of statistics, 43, 1498–1534.
   PubMed Web of Science ®Google Scholar
• Feng, Z., Wen, X. M., Yu, Z., and Zhu, L. (2013), “On Partial Sufficient Dimension Reduction with Applications to Partially Linear Multi-Index Models,” Journal of the American Statistical Association, 108, 237–246.
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2001), The Elements of Statistical Learning (Springer Series in Statistics, Vol. 1), Berlin: Springer.
   Google Scholar
• ——— (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
   PubMed Web of Science ®Google Scholar
• Fung, G. M., and Mangasarian, O. L. (2004), “A Feature Selection Newton Method for Support Vector Machine Classification,” Computational Optimization and Applications, 28, 185–202.
   Web of Science ®Google Scholar
• Goeman, J., Meijer, R., and Chaturvedi, N. (2012), “penalized: L1 (Lasso and Fused Lasso) and L2 (ridge) Penalized Estimation in GLMs and in the Cox Model,” CRAN R Package, R Foundation for Statistical Computing.
   Google Scholar
• Gupta, A. K., and Nagar, D. K. (1999), Matrix Variate Distributions (Vol. 104), Boca Raton, FL: CRC Press.
   Google Scholar
• Han, F., Zhao, T., and Liu, H. (2013), “Coda: High Dimensional Copula Discriminant Analysis,” Journal of Machine Learning Research, 14, 629–671.
   Web of Science ®Google Scholar
• Hand, D. J. (2006), “Classifier Technology and the Illusion of Progress,” Statistical Science, 21, 1–14.
   PubMed Web of Science ®Google Scholar
• Hastie, T., Tibshirani, R., and Wainwright, M. (2015), Statistical Learning with Sparsity: The Lasso and Generalizations, Boca Raton, FL: CRC Press.
   Google Scholar
• Hoff, P. D. (2015), “Multilinear Tensor Regression for Longitudinal Relational Data,” The Annals of Applied Statistics, 9, 1169–1193.
   PubMed Web of Science ®Google Scholar
• Jiang, B., Wang, X., and Leng, C. (2015), “QUDA: A Direct Approach for Sparse Quadratic Discriminant Analysis,” arXiv:1510.00084.
   Google Scholar
• Kolda, T. G., and Bader, B. W. (2009), “Tensor Decompositions and Applications,” SIAM Review, 51, 455–500.
   Web of Science ®Google Scholar
• Lai, Z., Xu, Y., Yang, J., Tang, J., and Zhang, D. (2013), “Sparse Tensor Discriminant Analysis,” IEEE Transactions on Image Processing, 22, 3904–3915.
   PubMed Web of Science ®Google Scholar
• Le, Y., and Hastie, T. (2014), “Sparse Quadratic Discriminant Analysis and Community Bayes,” arXiv:1407.4543.
   Google Scholar
• Ledoit, O., and Wolf, M. (2004), “A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices,” Journal of Multivariate Analysis, 88, 365–411.
   Web of Science ®Google Scholar
• Li, L., and Zhang, X. (2017), “Parsimonious Tensor Response Regression,” Journal of the American Statistical Association, 112, 1131–1146.
   Web of Science ®Google Scholar
• Li, Q., and Schonfeld, D. (2014), “Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 36, 2524–2537.
   PubMed Web of Science ®Google Scholar
• Li, Q., and Shao, J. (2015), “Sparse Quadratic Discriminant Analysis for High Dimensional Data,” Statistica Sinica, 25, 457–473.
   Web of Science ®Google Scholar
• Liaw, A., and Wiener, M. (2014), “Package ‘Randomforest’: Breiman and Cutler’s Random Forests for Classification and Regression,” CRAN R Package, R Foundation for Statistical Computing.
   Google Scholar
• Lin, Y., and Jeon, Y. (2003), “Discriminant Analysis through a Semiparametric Model,” Biometrika, 90, 379–392.
   Web of Science ®Google Scholar
• Liu, T., Yuan, M., and Zhao, H. (2017), “Characterizing Spatiotemporal Transcriptome of Human Brain via Low Rank Tensor Decomposition,” arXiv:1702.07449.
   Google Scholar
• Lock, E. F. (2018), “Tensor-on-Tensor Regression,” Journal of Computational and Graphical Statistics, accepted.
   PubMed Web of Science ®Google Scholar
• Mai, Q., Yang, Y., and Zou, H. (2018), “Multiclass Sparse Discriminant Analysis,” Statistica Sinica, accepted.
   Web of Science ®Google Scholar
• Mai, Q., and Zou, H. (2015), “Sparse Semiparametric Discriminant Analysis,” Journal of Multivariate Analysis, 135, 175–188.
   Web of Science ®Google Scholar
• Mai, Q., Zou, H., and Yuan, M. (2012), “A Direct Approach to Sparse Discriminant Analysis in Ultra-High Dimensions,” Biometrika, 99, 29–42.
   Web of Science ®Google Scholar
• Manceur, A. M., and Dutilleul, P. (2013), “Maximum Likelihood Estimation for the Tensor Normal Distribution: Algorithm, Minimum Sample Size, and Empirical Bias And Dispersion,” Journal of Computational and Applied Mathematics, 239, 37–49.
   Web of Science ®Google Scholar
• Michie, D., Spiegelhalter, D. J., and Taylor, C. C. (1994), Machine Learning, Neural and Statistical Classification, Glasgow, Scotland: Ellis Horwood.
   Google Scholar
• Pan, R., Wang, H., and Li, R. (2016), “Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening,” Journal of the American Statistical Association, 111, 169–179.
   PubMed Web of Science ®Google Scholar
• Raskutti, G., and Yuan, M. (2015), “Convex Regularization for High-Dimensional Tensor Regression,” arXiv:1512.01215.
   Google Scholar
• Shao, J., Wang, Y., Deng, X., and Wang, S. (2011), “Sparse Linear Discriminant Analysis by Thresholding for High Dimensional Data,” The Annals of Statistics, 39, 1241–1265.
   Web of Science ®Google Scholar
• Sun, W. W., Lu, J., Liu, H., and Cheng, G. (2016), “Provable Sparse Tensor Decomposition,” Journal of the Royal Statistical Society, Series B, 79, 899–916.
   Google Scholar
• Tao, D., Li, X., Wu, X., and Maybank, S. J. (2007), “General Tensor Discriminant Analysis and Gabor Features for Gait Recognition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 29, 1700–1715.
   PubMed Web of Science ®Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection Via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
   Google Scholar
• Wang, X., and Zhu, H. (2017), “Generalized Scalar-on-Image Regression Models via Total Variation,” Journal of the American Statistical Association, 112, 1156–1168.
   PubMed Web of Science ®Google Scholar
• Werner, K., Jansson, M., and Stoica, P. (2008), “On Estimation of Covariance Matrices with Kronecker Product Structure,” IEEE Transactions on Signal Processing, 56, 478–491.
   Web of Science ®Google Scholar
• Wimalawarne, K., Tomioka, R., and Sugiyama, M. (2016), “Theoretical and Experimental Analyses of Tensor-Based Regression and Classification,” Neural Computation, 28, 686–715.
   PubMed Web of Science ®Google Scholar
• Witten, D. M., and Tibshirani, R. (2011), “Penalized Classification using Fisher’s Linear Discriminant,” Journal of the Royal Statistical Society, Series B, 73, 753–772.
   Google Scholar
• Xu, P., Zhu, J., Zhu, L., and Li, Y. (2015), “Covariance-Enhanced Discriminant Analysis,” Biometrica, 102, 33–45.
   PubMed Web of Science ®Google Scholar
• Yan, S., Xu, D., Yang, Q., Zhang, L., Tang, X., and Zhang, H.-J. (2005), “Discriminant Analysis with Tensor Representation,” in 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), pp. 526–532, available at https://ieeexplore.ieee.org/.
   Google Scholar
• Yuan, M., and Lin, Y. (2006), “Model Selection and Estimation in Regression with Grouped Variables,” Journal of the Royal Statistical Society, Series B, 68, 49–67.
   Google Scholar
• Zeng, R., Wu, J., Senhadji, L., and Shu, H. (2015), “Tensor Object Classification via Multilinear Discriminant Analysis Network,” in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1971–1975, available at https://ieeexplore.ieee.org/.
   Google Scholar
• Zhang, A., and Xia, D. (2018), “Tensor SVD: Statistical and Computational Limits,” IEEE Transactions on Information Theory, accepted.
   PubMed Web of Science ®Google Scholar
• Zhang, X. (2013), “New Developments for Net-Effect Plots,” Wiley Interdisciplinary Reviews: Computational Statistics, 5, 105–113.
   Google Scholar
• Zhang, X., and Li, L. (2017), “Tensor Envelope Partial Least-Squares Regression,” Technometrics, 59, 426–436.
   Web of Science ®Google Scholar
• Zhao, J., and Leng, C. (2014), “Structured Lasso for Regression with Matrix Covariates,” Statistica Sinica, 24, 799–814.
   Web of Science ®Google Scholar
• Zhong, W., and Suslick, K. S. (2015), “Matrix Discriminant Analysis with Application to Colorimetric Sensor Array Data,” Technometrics, 57, 524–534.
   PubMed Web of Science ®Google Scholar
• Zhou, H., and Li, L. (2014), “Regularized Matrix Regression,” Journal of the Royal Statistical Society, Series B, 76, 463–483.
   Google Scholar
• Zhou, H., Li, L., and Zhu, H. (2013), “Tensor Regression with Applications in Neuroimaging Data Analysis,” Journal of the American Statistical Association, 108, 540–552.
   PubMed Web of Science ®Google Scholar
• Zhou, S. (2014), “Gemini: Graph Estimation with Matrix Variate Normal Instances,” The Annals of Statistics, 42, 532–562.
   Web of Science ®Google Scholar