We propose a novel multiple-instance learning (MIL) method to assess the visibility (visible/not visible) of the retinal nerve fiber layer (RNFL) in fundus camera images. Using only image-level labels, our approach learns to classify the images as well as to localize the RNFL visible regions. We transform the original feature space into a discriminative subspace, and learn a region-level classifier in that subspace. We propose a margin-based loss function to jointly learn this subspace and the region-level classifier. Experiments with an RNFL data set containing 884 images annotated by two ophthalmologists give a system-annotator agreement (kappa values) of 0.73 and 0.72, respectively, with an interannotator agreement of 0.73. Our system agrees better with the more experienced annotator. Comparative tests with three public data sets (MESSIDOR and DR for diabetic retinopathy, and UCSB for breast cancer) show that our novel MIL approach improves performance over the state of the art. Our MATLAB code is publicly available at https://github.com/ManiShiyam/Sub-categoryclassifiers-for-Multiple-Instance-Learning/wiki.