Title: Subspace Network: Deep Multi-Task Censored Regression for Modeling Neurodegenerative Diseases. Abstract: 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 extensively explored in these studies to address challenges associated to high dimensionality and small cohort size. 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 effects among the variables. In this paper, we propose the 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. We show that under mild assumptions, for each layer the parametric subspace can be recovered using only one pass of training data. In addition, empirical results demonstrate that the proposed subspace network quickly picks up correct parameter subspaces, and outperforms state-of-the-arts in predicting neurodegenerative clinical scores using information in brain imaging. 