High-Dimensional Longitudinal Classification with the Multinomial Fused Lasso
This work addresses classification in high-dimensional longitudinal data, such as Alzheimer's disease studies, but is incremental as it builds on existing lasso and fused lasso methods.
The authors tackled high-dimensional longitudinal classification by developing regularized estimation with lasso and fused lasso, resulting in piecewise constant coefficient estimates with adaptively selected change points, and applied it to an Alzheimer's disease dataset to address practical considerations like tuning parameter selection.
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.