TY - JOUR
T1 - Collaborative sliced inverse regression
AU - Chiancone, Alessandro
AU - Girard, Stéphane
AU - Chanussot, Jocelyn
PY - 2017/6/18
Y1 - 2017/6/18
N2 - Sliced inverse regression (SIR) is an effective method for dimensionality reduction in high-dimensional regression problems. However, the method has requirements on the distribution of the predictors that are hard to check since they depend on unobserved variables. It has been shown that, if the distribution of the predictors is elliptical, then these requirements are satisfied. In case of mixture models, the ellipticity is violated and in addition there is no assurance of a single underlying regression model among the different components. Our approach clusterizes the predictors space to force the condition to hold on each cluster and includes a merging technique to look for different underlying models in the data. A study on simulated data as well as two real applications are provided. It appears that SIR, unsurprisingly, is not capable of dealing with a mixture of Gaussians involving different underlying models whereas our approach is able to correctly investigate the mixture.
AB - Sliced inverse regression (SIR) is an effective method for dimensionality reduction in high-dimensional regression problems. However, the method has requirements on the distribution of the predictors that are hard to check since they depend on unobserved variables. It has been shown that, if the distribution of the predictors is elliptical, then these requirements are satisfied. In case of mixture models, the ellipticity is violated and in addition there is no assurance of a single underlying regression model among the different components. Our approach clusterizes the predictors space to force the condition to hold on each cluster and includes a merging technique to look for different underlying models in the data. A study on simulated data as well as two real applications are provided. It appears that SIR, unsurprisingly, is not capable of dealing with a mixture of Gaussians involving different underlying models whereas our approach is able to correctly investigate the mixture.
KW - Inverse regression
KW - mixture models
KW - sufficient dimension regression
UR - http://www.scopus.com/inward/record.url?scp=85014750658&partnerID=8YFLogxK
U2 - 10.1080/03610926.2015.1116578
DO - 10.1080/03610926.2015.1116578
M3 - Article
AN - SCOPUS:85014750658
SN - 0361-0926
VL - 46
SP - 6035
EP - 6053
JO - Communications in Statistics / Theory and Methods
JF - Communications in Statistics / Theory and Methods
IS - 12
ER -