We propose a novel multiple instance learning 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 to 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 a RNFL dataset containing 576 images annotated by two experienced ophthalmologists give an agreement (kappa values) of 0.65 and 0.58 respectively,with an inter-annotator agreement of 0.62. Note that our system gives higher agreements with the more experienced annotator. Comparative tests with three public datasets (MESSIDOR and DR for diabetic retinopathy,UCSB for breast cancer) show improved performance over the state-of-the-art.