Joint sparse and low-rank regularized multi-task multi-linear regression for prediction of infant brain development with incomplete data

Studies involving dynamic infant brain development has received increasing attention in the past few years. For such studies, a complete longitudinal dataset is often required to precisely chart the early brain developmental trajectories. Whereas, in practice, we often face missing data at different time point(s) for different subjects. In this paper, we propose a new method for prediction of infant brain development scores at future time points based on longitudinal imaging measures at early time points with possible missing data. We treat this as a multi-dimensional regression problem, for predicting multiple brain development scores (multi-task) from multiple previous time points (multi-linear). To solve this problem, we propose an objective function with a joint ℓ₁ and low-rank regularization on the mapping weight tensor, to enforce feature selection, while preserving the structural information from multiple dimensions. Also, based on the bag-of-words model, we propose to extract features from longitudinal imaging data. The experimental results reveal that we can effectively predict the brain development scores assessed at the age of four years, using the imaging data as early as two years of age.