  Over the past decade a wide spectrum of machine learning models have been
developed to model the neurodegenerative diseases, associating biomarkers,
especially non-intrusive neuroimaging markers, with key clinical scores
measuring the cognitive status of patients. Multi-task learning (MTL) has been
commonly utilized by these studies to address high dimensionality and small
cohort size challenges. However, most existing MTL approaches are based on
linear models and suffer from two major limitations: 1) they cannot explicitly
consider upper/lower bounds in these clinical scores; 2) they lack the
capability to capture complicated non-linear interactions among the variables.
In this paper, we propose Subspace Network, an efficient deep modeling approach
for non-linear multi-task censored regression. Each layer of the subspace
network performs a multi-task censored regression to improve upon the
predictions from the last layer via sketching a low-dimensional subspace to
perform knowledge transfer among learning tasks. Under mild assumptions, for
each layer the parametric subspace can be recovered using only one pass of
training data. Empirical results demonstrate that the proposed subspace network
quickly picks up the correct parameter subspaces, and outperforms
state-of-the-arts in predicting neurodegenerative clinical scores using
information in brain imaging.
