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Accurate diagnosis of Alzheimer's disease and its prodromal stage, i.e., mild cognitive impairment, is very important for early treatment. Over the last decade, various machine learning methods have been proposed to predict disease status and clinical scores from brain images. It is worth noting that many features extracted from brain images are correlated significantly. In this case, feature selection combined with the additional correlation information among features can effectively improve classification/regression performance. Typically, the correlation information among features can be modeled by the connectivity of an undirected graph, where each node represents one feature and each edge indicates that the two involved features are correlated significantly. In this paper, we propose a new graph-guided multi-task learning method incorporating this undirected graph information to predict multiple response variables (i.e., class label and clinical scores) jointly. Specifically, based on the sparse undirected feature graph, we utilize a new latent group Lasso penalty to encourage the correlated features to be selected together. Furthermore, this new penalty also encourages the intrinsic correlated tasks to share a common feature subset. To validate our method, we have performed many numerical studies using simulated datasets and the Alzheimer's Disease Neuroimaging Initiative dataset. Compared with the other methods, our proposed method has very promising performance.

Graph-guided joint prediction of class label and clinical scores for the Alzheimer’s disease