  In a regression setting we propose algorithms that reduce the dimensionality
of the features while simultaneously maximizing a statistical measure of
dependence known as distance correlation between the low-dimensional features
and a response variable. This helps in solving the prediction problem with a
low-dimensional set of features. Our setting is different from subset-selection
algorithms where the problem is to choose the best subset of features for
regression. Instead, we attempt to generate a new set of low-dimensional
features as in a feature-learning setting. We attempt to keep our proposed
approach as model-free and our algorithm does not assume the application of any
specific regression model in conjunction with the low-dimensional features that
it learns. The algorithm is iterative and is fomulated as a combination of the
majorization-minimization and concave-convex optimization procedures. We also
present spectral radius based convergence results for the proposed iterations.
