# [BNS17] Prediction for regularized clusterwise multiblock regression

**Conférence Internationale avec comité de lecture : **
ASMDA 2017,
June 2017,

pp.42-43,
Londres,
UK,

**Mots clés: ** multiblock analysis, clusterwise regression, multiblock discriminant analysis, supervised multiblock classification.

**Résumé: **
Multiblock methods integrate the information in several blocks of explanatory variables to explain a set of dependent variables. However in many applications, multiblock techniques are used when the observations come from a homogeneous population but it often happens that the observations originate from different ones. A standard approach to obtain clusters within a regression framework is clusterwise, a.k.a. typological, regression. These methods assume that there is an underlying unknown group structure of the observations and that each cluster can be revealed by the fit of a specific regression model. In a more formal way, clusterwise regression simultaneously looks for a partition of the observations into clusters and minimizes the sum of squared errors computed over all the clusters.
We propose to combine a regularized multiblock regression with a clusterwise approach. We focus on prediction as a matter of utmost importance however not addressed in the clusterwise framework. In practice, clusterwise prediction can be used for two major goals: (i) the prediction of new observations and (ii) the selection of the unknown parameters of the clusterwise multiblock regression, i.e. the number of clusters, the number of number of components to be included in the model and the regularization parameter value, while minimizing the cross-validated prediction error. For this purpose, several original multiblock supervised classifications are checked in the field of clusterwise analysis. A simulation study is carried out to assess the prediction method performances and an empirical application is provided to illustrate the method usefulness.

Collaboration:
ANSES