  High-dimensional prediction is a challenging problem setting for traditional
statistical models. Although regularization improves model performance in high
dimensions, it does not sufficiently leverage knowledge on feature importances
held by domain experts. As an alternative to standard regularization
techniques, we propose Distance Metric Learning Regularization (DMLreg), an
approach for eliciting prior knowledge from domain experts and integrating that
knowledge into a regularized linear model. First, we learn a Mahalanobis
distance metric between observations from pairwise similarity comparisons
provided by an expert. Then, we use the learned distance metric to place prior
distributions on coefficients in a linear model. Through experimental results
on a simulated high-dimensional prediction problem, we show that DMLreg leads
to improvements in model performance when the domain expert is knowledgeable.
