  We study regularized estimation in high-dimensional longitudinal
classification problems, using the lasso and fused lasso regularizers. The
constructed coefficient estimates are piecewise constant across the time
dimension in the longitudinal problem, with adaptively selected change points
(break points). We present an efficient algorithm for computing such estimates,
based on proximal gradient descent. We apply our proposed technique to a
longitudinal data set on Alzheimer's disease from the Cardiovascular Health
Study Cognition Study, and use this data set to motivate and demonstrate
several practical considerations such as the selection of tuning parameters,
and the assessment of model stability.
