Réduction de dimension dans les modèles linéaires généralisés : application à la classification supervisée de données issues des biopuces
Journal de la société française de statistique, Volume 146 (2005) no. 1-2, p. 117-152
@article{JSFS_2005__146_1-2_117_0,
     author = {Fort, Gersende and Lambert-Lacroix, Sophie and Peyre, Julie},
     title = {R\'eduction de dimension dans les mod\`eles lin\'eaires g\'en\'eralis\'es : application \`a la classification supervis\'ee de donn\'ees issues des biopuces},
     journal = {Journal de la soci\'et\'e fran\c caise de statistique},
     publisher = {Soci\'et\'e fran\c caise de statistique},
     volume = {146},
     number = {1-2},
     year = {2005},
     pages = {117-152},
     language = {fr},
     url = {http://www.numdam.org/item/JSFS_2005__146_1-2_117_0}
}
Fort, Gersende; Lambert-Lacroix, Sophie; Peyre, Julie. Réduction de dimension dans les modèles linéaires généralisés : application à la classification supervisée de données issues des biopuces. Journal de la société française de statistique, Volume 146 (2005) no. 1-2, pp. 117-152. http://www.numdam.org/item/JSFS_2005__146_1-2_117_0/

Albert A., Anderson J. (1984). On the Existence of Maximum Likelihood Estimates in Logistic Regression Models. Biometrika, 71(1) :1-10. | MR 738319 | Zbl 0543.62020

Alon U., Barkai N., Notterman D., Gish K., Ybarra S., Mack D., Levine A. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Natl. Acad. Sci. USA, 96(12) :6745-6750.

Antoniadis A., Lambert-Lacroix S., Leblanc F. (2003). Effective Dimension Reduction Methods for Tumor - Classification using gene Expression Data. Bioinformatics, 19(5) :563-570.

Barker M., Rayens W. (2003). Partial least squares for discrimination. J. Chemometrics, 17 :166-173.

Bastien P. (2004). PLS-Cox model : application to gene expression. Dans Proceedings in Computational Statistics, pages 655-662. Physica-Verlag, Springer. | MR 2173059

Bastien P., Esposito Vinzi V., Tenenhaus M. (2004). PLS generalised linear regression. Comput. Stat. Data Anal., 48(1) :17-46. | MR 2133599 | Zbl pre05374090

Bull S., Mak C., Greenwood C. (2001). A modified score function estimator for multinomial logistic regression is small samples. Comput. Stat. Data Anal., 39 :57-74. | Zbl 1119.62344

Dejong S. (1995). PLS shrinks. J. Chemometrics, 9 :323-326.

Denham M. (2000). Choosing the number of factors in partial least squares regression : estimating and minimizing the mean squared error of prediction. J. Chemometrics, 14 :351-361.

Devroye L., Gyorfi L., Lugosi G. (1996). A Probabilistic Theory of Pattern Recognition. Springer-Verlag, New-York. | MR 1383093 | Zbl 0853.68150

Ding B., Gentleman R. (2005). Classification Using Generalized Partial Least Squares. J. Comp. Graph. Stat. À paraître. | MR 2160814

Dudoit S., Fridlyand J., Speed T. (2002). Comparison of discrimination methods for the classification of tumors using gene expression data. J. Am. Stat. Assoc., 97(457) :77-87. | MR 1963389 | Zbl 1073.62576

Efron B., Hastie T., Johnstone I., Tibshirani R. (2004). Least angle regression. Ann. Stat., 32(2) :407-499. | MR 2060166 | Zbl 1091.62054

Fahrmeir L., Tutz G. (2001). Multivariate statistical modelling based on generalized linear models. 2nd ed. Springer Series in Statistics. New York. | MR 1832899 | Zbl 0980.62052

Fan J., Gijbels I. (1996). Local polynomial modelling and its applications. Monographs on Statistics and Applied Probability. Chapman and Hall, London. | MR 1383587 | Zbl 0873.62037

Fort G. (2005). Partial Least Squares for Classification and Feature selection in Microarray gene expression data. Soumis.

Fort G., Lambert-Lacroix S. (2005). Classification using Partial Least Squares with Penalized Logistic Regression. Bioinformatics, 21(7) :1104-1111.

Frank I., Friedman J. (1993). A statistical view of some chemometrics regression tools, with discussion. Technometrics, 35(2) :109-148. | Zbl 0775.62288

Garthwaite P. (1994). An interpretation of partial least squares. J. Am. Stat. Assoc., 89(425) :122-127. | MR 1266290 | Zbl 0793.62034

Golub T., Slonim D., Tamayo P., Huard C., Gaasenbeek M., Mesirov J., Coller H., Loh M., Downing J., Caligiuri M., Bloomfield C., Lander E. (1999). Molecular Classification of Cancer : Class Discovery and Class Prediction by Gene Expression Monitoring. Science, 286(5439) :531-537.

Goutis C. (1996). Partial Least Squares algorithm yields shrinkage estimators. Ann. Stat., 24(2) :816-824. | MR 1394990 | Zbl 0859.62067

Green P. (1984). Iteratively Reweighted Least Squares for Maximum Likelihood Estimation, and some Robust and Resistant Alternatives. J. R. Stat. Soc., Ser. B, 46(2) :149-192. | MR 781879 | Zbl 0555.62028

Guyon I., Weston J., Barnhill S., Vapnik V. (2002). Gene Selection for Cancer Classification using Support Vector Machines. Mach. Learn., 46(1-3) :389-422. Erratum : http://clopinet.com/isabelle/Papers/index.html. | Zbl 0998.68111

Hastie T., Tibshirani R. (1990). Generalized Additive Models. Monographs on Statistics and Applied Probability. New York : Chapman and Hall. | MR 1082147 | Zbl 0747.62061

Hastie T., Tibshirani R., Eisen M., Alizadeh A., Levy R., Staudt L., Chan W., Botstein D., Brown P. (2000). 'gene shaving' as a method for identifying distinct sets of genes with similar expression patterns. Genome Biol., 1.

Helland I. (1988). On the structure of Partial Least Squares regression. Commun. Stat. Simulation Comput., 17(2) :581-607. | MR 955342 | Zbl 0695.62167

Helland I. (1990). Partial Least Squares Regression and Statistical Models. Scand. J. Statist., 17(2) :97-114. | MR 1085924 | Zbl 0713.62062

Kuo W., Kim E., Trimarchi B., Jenssen J., Vinterbo T., Ohno-Machado L. (2004). Bayes factor. J. Biomed. Inform., 37 :293-303.

Lambert-Lacroix S., Peyre J. (2005). Local quasi-likelihood regression in generalized single-index models. Travaux en cours.

Lesaffre E., Albert A. (1989). Partial separation in logistic discrimination. J. R. Stat. Soc., Ser. B, 51(1) :109-116. | MR 984997 | Zbl 0669.62044

Lingjaerde O., Christophersen N. (2000). Shrinkage structure of Partial Least Squares. Scand. J. Stat., 27 :459-473. | MR 1795775 | Zbl 0972.62044

Marx B. D. (1996). Iteratively Reweighted Partial Least Squares estimation for Generalized Linear Regression. Technometrics, 38(4) :374-381. | Zbl 0902.62081

Nguyen D., Rocke D. ( 2002a). Multi-class cancer classification via Partial Least Squares with gene expression profiles. Bioinformatics, 18(9) :1116-1226.

Nguyen D., Rocke D. ( 2002b). Tumor classification by Partial Least Squares using microarray gene expression data. Bioinformatics, 18(1) :39-50.

Nguyen D., Rocke D. (2004). On partial least squares dimension reduction for microarray-based classification : a simulation study. Comput. Stat. Data Anal., 46 :407-425. | MR 2067030 | Zbl 05374013 | Zbl pre05374013

Phatak A., Reilly P., Penlidis A. (2002). The asymptotic variance of the univariate PLS estimator. Linear Algebra Appl., 354(1-3) :245-253. | MR 1927660 | Zbl 1022.62024

Santner T., Duffy D. (1986). A note on A. Albert and J.A. Anderson's Conditions for the Existence of Maximum Likelihood Estimates in Logistic Regression Models. Biometrika, 73(3) :755-758. | MR 897873 | Zbl 0655.62022

Saporta G. (1990). Probabilités, analyse des données et statistique. Paris : Éditions Technip. | Zbl 0703.62003

Schwarz G. (1978). Estimating the dimension of a model. Ann. Stat., 6(2) :461-464. | MR 468014 | Zbl 0379.62005

Seifert B., Gasser T. (1996). Finite sample variance of local polynomials : Analysis and solutions. J. Am. Stat. Assoc., 91(433) :267-275. | MR 1394081 | Zbl 0871.62042

Stoica P., Soderstrom T. (1998). Partial Least Squares : A First-order Analysis. Scand. J. Stat., 25(1) :17-24. | MR 1614231 | Zbl 0903.62057

Stone M., Brooks R. (1990). Continuum regression : Cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and principal components regression. J. R. Stat. Soc., Ser. B, 52(2) :237-269. | MR 1064418 | Zbl 0708.62054

Tibshirani R. (1996). Regression Shrinkage and Selection via the Lasso. J. R. Stat. Soc., Ser. B, 58(1) :267-288. | MR 1379242 | Zbl 0850.62538

Xia Y., Tong H., Li W., Zhu L. (2002). An adaptive estimation of dimension reduction space. J. R. Stat. Soc., Ser. B, 64(3) :363-410. | MR 1924297 | Zbl 1091.62028

Zhu J., Hastie T. (2004). Classification of Gene Microarrays by Penalized Logistic Regression. Biostatistics, 5 :427-443. | Zbl 1154.62406

Zou H., Hastie T. (2005). Regularization and Variable Selection via the Elastic Net. J. R. Stat. Soc., Ser. B, 67(2) :301-320. | MR 2137327 | Zbl 1069.62054