In many regression problems, different subgroups of the population exhibit different behavior with respect to the same covariates, To account for such cases where the regression parameter between the response and the covariates can differ from subject to subject, depending on the values of a set of classification variables, the change plane model can be aptly used. Although this model has been studied and seen application in bio-medicine and econometrics, with the growing size of datasets, change plane models with high dimensional variables now warrants attention. However, the key challenge of such an extension is that change plane estimation would involve optimization over non-continuous expressions, To deal with this, we propose a method which involves convex optimization over proxy expressions which are arbitrarily close to the true optimization problem, with the proxy optimizers also converging to the true parameter of interest. Additionally, we find that adaptive sampling techniques, which work for low dimensional change-point problems and drastically cut down on estimation time, can also be extended to this model.
Joint work with Moulinath Banerjee and Ya'acov Ritov.