A model is presented for the supervised learning problem where the observations come from a fixed number of pre-specified groups, and the regression coefficients may vary sparsely between groups. The model spans the continuum between individual models for each group and one model for all groups. The resulting algorithm is designed with a high dimensional framework in mind. The approach is applied to a sentiment analysis dataset to show its efficacy and interpretability. One particularly useful application is for finding sub-populations in a randomized trial for which an intervention (treatment) is beneficial, often called the uplift problem. Some new concepts are introduced that are useful for uplift analysis. The value is demonstrated in an application to a real world credit card promotion dataset. In this example, although sending the promotion has a very small average effect, by targeting a particular subgroup with the promotion one can obtain a 15% increase in the proportion of people who purchase the new credit card.