Predicting glaucoma progression using multi-task learning with heterogeneous features

We consider the prediction of glaucomatous visual field loss based on patient datasets. It is critically important to predict how rapidly the disease is progressing in an individual patient. However, the number of measurements for each patient is so small that a reliable predictor cannot be constructed from the data of a single patient alone. In this paper, we propose a novel multi-task learning approach to this issue. Patient data consist of three features: patient ID, 74-dimensional visual loss values, and inspection time. We reduce the prediction problem into one of matrix completion for these features. Specifically, by assuming heterogeneity in the three features, we introduce similarity measures that reflect the unique statistical nature of the respective features to solve a specific type of matrix decomposition problem. For example, we employ Gaussian kernels as a similarity measure for visual field loss and a linear regression-type relation for the time feature. We empirically demonstrate that our proposed method works significantly better than the existing methods.