### Abstract

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.

Language | English |
---|---|

Pages | 6035-6053 |

Number of pages | 19 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 46 |

Issue number | 12 |

DOIs | |

Status | Published - 18 Jun 2017 |

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### Keywords

- Inverse regression
- mixture models
- sufficient dimension regression

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*46*(12), 6035-6053. DOI: 10.1080/03610926.2015.1116578

**Collaborative sliced inverse regression.** / Chiancone, Alessandro; Girard, Stéphane; Chanussot, Jocelyn.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol 46, no. 12, pp. 6035-6053. DOI: 10.1080/03610926.2015.1116578

}

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

VL - 46

SP - 6035

EP - 6053

JO - Communications in statistics / Theory and methods

T2 - Communications in statistics / Theory and methods

JF - Communications in statistics / Theory and methods

SN - 0361-0926

IS - 12

ER -