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Variable and boundary selection for functional data via multiclass logistic regression modeling

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  • Matsui, Hidetoshi

Abstract

Penalties with an ℓ1 norm provide solutions in which some coefficients are exactly zero and can be used for selecting variables in regression settings. When applied to the logistic regression model, they also can be used to select variables which affect classification. We focus on the form of ℓ1 penalties in logistic regression models for functional data, in particular, their use in classifying functions into three or more groups while simultaneously selecting variables or classification boundaries. We provide penalties that appropriately select the variables in functional multiclass logistic regression models. Analysis of simulation and real data show that the form of the penalty should be selected in accordance with the purpose of the analysis.

Suggested Citation

  • Matsui, Hidetoshi, 2014. "Variable and boundary selection for functional data via multiclass logistic regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 176-185.
    • Handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:176-185
    DOI: 10.1016/j.csda.2014.04.015
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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Li, Yehua & Wang, Naisyin & Carroll, Raymond J., 2010. "Generalized Functional Linear Models With Semiparametric Single-Index Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 621-633.
    3. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    4. Escabias, M. & Aguilera, A.M. & Valderrama, M.J., 2007. "Functional PLS logit regression model," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4891-4902, June.
    5. Philip T. Reiss & R. Todd Ogden, 2010. "Functional Generalized Linear Models with Images as Predictors," Biometrics, The International Biometric Society, vol. 66(1), pages 61-69, March.
    6. Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.
    7. F. Ferraty & P. Hall & P. Vieu, 2010. "Most-predictive design points for functional data predictors," Biometrika, Biometrika Trust, vol. 97(4), pages 807-824.
    8. Sadanori Konishi, 2004. "Bayesian information criteria and smoothing parameter selection in radial basis function networks," Biometrika, Biometrika Trust, vol. 91(1), pages 27-43, March.
    9. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    10. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
    11. repec:cte:wsrepe:ws131413 is not listed on IDEAS
    12. Yuko Araki & Sadanori Konishi & Shuichi Kawano & Hidetoshi Matsui, 2009. "Functional regression modeling via regularized Gaussian basis expansions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 811-833, December.
    13. Matsui, Hidetoshi & Konishi, Sadanori, 2011. "Variable selection for functional regression models via the L1 regularization," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3304-3310, December.
    14. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    15. M. Aguilera-Morillo & Ana Aguilera & Manuel Escabias & Mariano Valderrama, 2013. "Penalized spline approaches for functional logit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 251-277, June.
    16. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    17. Gareth M. James, 2002. "Generalized linear models with functional predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 411-432, August.
    18. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    19. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    20. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    2. Gregorutti, Baptiste & Michel, Bertrand & Saint-Pierre, Philippe, 2015. "Grouped variable importance with random forests and application to multiple functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 15-35.
    3. Mirosław Krzyśko & Łukasz Smaga, 2017. "An Application Of Functional Multivariate Regression Model To Multiclass Classification," Statistics in Transition New Series, Polish Statistical Association, vol. 18(3), pages 433-442, September.
    4. Łukasz Smaga & Hidetoshi Matsui, 2018. "A note on variable selection in functional regression via random subspace method," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 455-477, August.
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    6. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
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    8. Andreas Groll & Trevor Hastie & Gerhard Tutz, 2017. "Selection of effects in Cox frailty models by regularization methods," Biometrics, The International Biometric Society, vol. 73(3), pages 846-856, September.
    9. Krzyśko Mirosław & Smaga Łukasz, 2017. "An Application of Functional Multivariate Regression Model to Multiclass Classification," Statistics in Transition New Series, Statistics Poland, vol. 18(3), pages 433-442, September.

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