  When faced with a supervised learning problem, we hope to have rich enough
data to build a model that predicts future instances well. However, in
practice, problems can exhibit predictive heterogeneity: most instances might
be relatively easy to predict, while others might be predictive outliers for
which a model trained on the entire dataset does not perform well. Identifying
these can help focus future data collection. We present gLOP, the global and
Local Penalty, a framework for capturing predictive heterogeneity and
identifying predictive outliers. gLOP is based on penalized regression for
multitask learning, which improves learning by leveraging training signal
information from related tasks. We give two optimization algorithms for gLOP,
one space-efficient, and another giving the full regularization path. We also
characterize uniqueness in terms of the data and tuning parameters, and present
empirical results on synthetic data and on two health research problems.
