  Sparse alpha-norm regularization has many data-rich applications in Marketing
and Economics. Alpha-norm, in contrast to lasso and ridge regularization, jumps
to a sparse solution. This feature is attractive for ultra high-dimensional
problems that occur in demand estimation and forecasting. The alpha-norm
objective is nonconvex and requires coordinate descent and proximal operators
to find the sparse solution. We study a typical marketing demand forecasting
problem, grocery store sales for salty snacks, that has many dummy variables as
controls. The key predictors of demand include price, equivalized volume,
promotion, flavor, scent, and brand effects. By comparing with many commonly
used machine learning methods, alpha-norm regularization achieves its goal of
providing accurate out-of-sample estimates for the promotion lift effects.
Finally, we conclude with directions for future research.
