Title: Bayesian approach for uplift linear regression
Authors: Yuji Iikubo - Waseda University (Japan) [presenting]
Shunsuke Horii - Waseda University (Japan)
Toshiyasu Matsushima - Waseda University (Japan)
Abstract: Uplift modeling is an important method for predicting the difference in effect when an action is taken and when it is not taken. Previously, many studies for uplift modeling have focused on the classification problem. However, their performances have been evaluated experimentally due to the difficulty of theoretical analysis. On the other hand, a few studies have focused on regression problems for theoretical analysis. The proposed estimators are unbiased and asymptotically normal, and they have focused on reducing the variance of the estimators. We propose a Bayesian approach for uplift linear regression. Assuming multivariate normal distributions for the prior distributions of the parameters, we show that the Bayes optimal estimator and predictor can be obtained in closed forms. In uplift modeling problems, another important issue is to determine the assignments of actions to estimate efficiently with small amounts of data. One of the advantages of the Bayesian approach is that you can obtain the posterior distributions of the parameter and the predictor. We also propose a sequential experimental design method by taking advantage of the Bayesian approach. Finally, we show the effectiveness of the proposed methods by numerical experiments using synthetic data and semi-synthetic data.