Nonparametric discriminant analysis with network structures in predictor

References

• Bagirov AM, Ferguson B, Ivkovic S, et al. New algorithms for multi-class cancer diagnosis using tumor gene expression signatures. Bioinformatics. 2003;19:1800–1807.
   PubMed Web of Science ®Google Scholar
• Bicciato S, Luchini A, Bello CD. PCA disjoint models for multiclass cancer analysis using gene expression data. Bioinformatics. 2003;19:571–578.
   PubMed Web of Science ®Google Scholar
• Liu JJ, Cutler G, Li W, et al. Multiclass cancer classification and biomarker discovery using GA-based algorithms. Bioinformatics. 2005;21:2691–2697.
   PubMed Web of Science ®Google Scholar
• Clemmensen L, Hastie T, Witten D, et al. Sparse discriminant analysis. Technometrics. 2011;53:406–413.
   Web of Science ®Google Scholar
• Witten DM, Tibshirani R. Penalized classification using Fisher's linear discriminant. J R Stat Soc Series B. 2011;73:753–772.
   Google Scholar
• Ramey JA, Stein CK, Young PD, et al. High-dimensional regularized discriminant analysis. 2017. arXiv:1602.01182.
   Google Scholar
• Bouveyron C, Girard S, Schmid C. High-dimensional discriminant analysis. Commun Stat Theory Methods. 2007;36:2607–2623.
   Web of Science ®Google Scholar
• Kolar M, Liu H. Optimal feature selection in high-dimensional discriminant analysis. IEEE Trans Inf Theory. 2015;61:1063–1083.
   PubMed Web of Science ®Google Scholar
• Mai Q, Zou H, Yuan M. A direct approach to sparse discriminant analysis in ultra-high dimensions. Biometrika. 2012;99:29–42.
   Web of Science ®Google Scholar
• Cai TT, Zhang L. High dimensional linear discriminant analysis: optimality, adaptive algorithm and missing data. J R Stat Soc Series B. 2019;81:675–705.
   Google Scholar
• Sifaou H, Kammoun A, Alouini M-S. High-dimensional linear discriminant analysis classifier for spiked covariance model. J Mach Learn Res. 2020;21:1–24.
   PubMed Web of Science ®Google Scholar
• Fan J, Li R, Zhang C-H, et al. Statistical foundations of data science. New York: CRC Press; 2021.
   Google Scholar
• Ye J, Ji S, Chen J. Multi-class discriminant kernel learning via convex programming. J Mach Learn Res. 2008;9:719–758.
   Web of Science ®Google Scholar
• Hidaka A, Kurita T. Nonlinear discriminant analysis based on probability estimation by Gaussian mixture model. In: Frnti P., Brown G., Loog M., Escolano F., Pelillo M. editors Structural, Syntactic, and Statistical Pattern Recognition. S+SSPR 2014; Berlin, Heidelberg: Springer; 2014. p. 133–142. (Lecture Notes in Computer Science; vol. 8621).
   Google Scholar
• George CM, Chijioke JN. Discriminant analysis with mixed non normal variables. Commun Stat Theory Methods. 2021. doi:10.1080/03610926.2021.1908563.
   Web of Science ®Google Scholar
• Chen L-P. Multiclassification to gene expression data with some complex features. Biostat Biom Open Access J. 2018;9:Article ID 555751.
   Google Scholar
• Cai W, Guan G, Pan R, et al. Network linear discriminant analysis. Comput Stat Data Anal. 2018;117:32–44.
   Web of Science ®Google Scholar
• Chen L-P, Yi GY, Zhang Q, et al. Multiclass analysis and prediction with network structured covariates. J Stat Distrib Appl. 2019;6(6). doi:10.1186/s40488-019-0094-2.
   Google Scholar
• He W, Yi GY, Chen L-P. Support vector machine with graphical network structures in features. Proceedings, Machine Learning and Data Mining in Pattern Recognition, 15th International Conference on Machine Learning and Data Mining, MLDM 2019, vol.II, New York, NY, USA, ibai-publishing, 557–570; 2019.
   Google Scholar
• Chen L-P. Network-based discriminant analysis for multiclassification. J Classif. 2022;to appear:1–22 doi:10.1007/s00357-022-09414-y.
   Google Scholar
• Bielza C, Li G, Larrañaga P. Multi-dimensional classification with Bayesian networks. Int J Approx Reason. 2011;52:705–727.
   Web of Science ®Google Scholar
• Miguel Hernández-Lobato J, Hernández-Lobato D, Suárez A. Network-based sparse Bayesian classification. Pattern Recognit. 2011;44:886–900.
   Web of Science ®Google Scholar
• Baladanddayuthapani V, Talluri R, Ji Y, et al. Bayesian sparse graphical models for classification with application to protein expression data. Ann Appl Stat. 2014;8:1443–1468.
   PubMed Web of Science ®Google Scholar
• Peterson CB, Stingo FC, Vannucci M. Joint Bayesian variable and graph selection for regression models with network-structured predictors. Stat Med. 2015;35:1017–1031.
   PubMed Web of Science ®Google Scholar
• Hastie T, Tibshirani R, Friedman J. The elements of statistical learning: data mining, inference, and prediction. New York: Springer; 2008.
   Google Scholar
• James G, Witten D, Hastie T, et al. An introduction to statistical learning: with applications in R hardcover. New York: Springer; 2017.
   Google Scholar
• Walpole R, Myers R, Myers S, et al. Probability & statistics for engineers & scientists. New York: Pearson; 2016.
   Google Scholar
• Yang E, Ravikumar P, Allen GI, et al. Graphical models via univariate exponential family distribution. J Mach Learn Res. 2015;16:3813–3847.
   PubMed Web of Science ®Google Scholar
• Hastie T, Tibshirani R, Wainwright M. Statistical learning with sparsity: the lasso and generalizations. New York: CRC press; 2015.
   Google Scholar
• Ravikumar P, Wainwright MJ, Lafferty J. High-dimensional Ising model selection using ℓ1-regularized logistic regression. Ann Stat. 2010;38:1287–1319.
   Web of Science ®Google Scholar
• Meinshausen N, Bühlmann P. High-dimensional graphs and variable selection with the lasso. Ann Stat. 2006;34:1436–1462.
   Web of Science ®Google Scholar
• Zou H. The adaptive lasso and its oracle properties. J Am Stat Assoc. 2006;101:1418–1429.
   Web of Science ®Google Scholar
• Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc. 2001;96:1348–1360.
   Web of Science ®Google Scholar
• Tibshirani R. Regression shrinkage and selection via the lasso. J R Stat Soc Series B. 1996;58:267–288.
   Google Scholar
• Zhao T, Liu H, Roeder K, et al. The huge package for high-dimensional undirected graph estimation in R. J Mach Learn Res. 2012;13:1059–1062.
   PubMed Web of Science ®Google Scholar
• Wan Y-W, Allen GI, Baker Y, et al. XMRF: an R package to fit Markov networks to high-throughput genetics data. BMC Syst Biol. 2016;10(Suppl 3):Article ID 69.
   Google Scholar
• Wang H, Li R, Tsai C. Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika. 2007;94:553–568.
   PubMed Web of Science ®Google Scholar
• Chen L-P, Yi GY. Analysis of noisy survival data with graphical proportional hazards measurement error models. Biometrics. 2021;77:956–969.
   PubMed Web of Science ®Google Scholar
• Schwarz G. Estimating the dimension of model. Ann Stat. 1978;6:461–464.
   Web of Science ®Google Scholar
• Hubert L, Arabie P. Comparing partitions. J Classif. 1985;2:193–218.
   Web of Science ®Google Scholar
• Chen L-P. Investigating effects of bandwidth selection in local polynomial regression model with applications. Model Assist Stat Appl. 2019;14:31–45.
   Google Scholar
• Chatterjee S, Diaconis P. Estimating and understanding exponential random graph models. Ann Stat. 2013;41:2428–2461.
   Web of Science ®Google Scholar
• Chatterjee S, Diaconis P, Sly A. Random graphs with a given degree sequence. Ann Appl Probab. 2011;21:1400–1435.
   Web of Science ®Google Scholar
• Yan T, Xu J. A central limit theorem in the β-model for undirected random graphs with a diverging number of vertices. Biometrika. 2013;100:519–524.
   Web of Science ®Google Scholar
• Snijders TAB. Markov chain Monte Carlo estimation of exponential random graph models. J Soc Struct. 2002;3(2):1–40.
   Google Scholar
• Handcock MS. Assessing degeneracy in statistical models of social networks. Working Paper no. 39, Center for Statistics and the Social Sciences, University of Washington; 2003. Available online at https://csss.uw.edu/Papers/wp39.pdf.
   Google Scholar
• Hunter DR, Handcock MS. Inference in curved exponential family models for networks. J Comput Graph Stat. 2006;15:565–583.
   Web of Science ®Google Scholar
• Yan T, Leng C, Zhu J. Asymptotics in directed exponential random graph models with an increasing bi-degree sequence. Ann Stat. 2016;44:31–57.
   Web of Science ®Google Scholar
• Hillar C, Wibisono A. Maximum entropy distributions on graphs. 2013. arXiv preprint arXiv:1301.3321.
   Google Scholar
• Yan T, Zhao Y, Qin H. Asymptotic normality in the maximum entropy distributions on graphs with an growing number of parameters. J Multivar Anal. 2015;133:61–76.
   Web of Science ®Google Scholar