Iterative Multivariate Regression Model for Correlated Responses Prediction

In the service oriented industry, a group of customers may be targeted for a set of marketing interests, and these interests are usually inter-correlated. For example, churn, upselling and appetency are often considered together, and decisions on how to retain customers, and to promote or to upgrade services are associated. Instead of predicting them separately as univariate models, we propose an iterative procedure to model multiple responses prediction into correlated multivariate predicting scheme. This proposed method combines Partial Least Squares (PLS) method and logistic regressions, in which the former is used to extract the mutual information from correlations, while the latter is utilized to refine every single response prediction through auxiliary information from PLS. This hybrid regression modeling is implemented iteratively to refine the prediction gradually. More importantly, to exploit the positive exclusive property (i.e., positive for one response means negative for the others) between multivariate responses, before every round of iteration, all the positive predictions from the different responses compete each other and only the highest values are kept for positive predictions and the remaining is changed to negative. Numerical results show the proposed scheme can improve the conventional regression models significantly.