  Multi-task learning is a type of transfer learning that trains multiple tasks
simultaneously and leverages the shared information between related tasks to
improve the generalization performance. However, missing features in the input
matrix is a much more difficult problem which needs to be carefully addressed.
Removing records with missing values can significantly reduce the sample size,
which is impractical for datasets with large percentage of missing values.
Popular imputation methods often distort the covariance structure of the data,
which causes inaccurate inference. In this paper we propose using plug-in
covariance matrix estimators to tackle the challenge of missing features.
Specifically, we analyze the plug-in estimators under the framework of robust
multi-task learning with LASSO and graph regularization, which captures the
relatedness between tasks via graph regularization. We use the Alzheimer's
disease progression dataset as an example to show how the proposed framework is
effective for prediction and model estimation when missing data is present.
