We propose a robust recommender systems model which performs matrix completion and a ratings-wise uncertainty estimation jointly. Whilst the prediction module is purely based on an implicit low-rank assumption imposed via nuclear norm regularization, our loss function is augmented by an uncertainty estimation module which learns an anomaly score for each individual rating via a Graph Neural Network: data points deemed more anomalous by the GNN are downregulated in the loss function used to train the low-rank module. The whole model is trained in an end-to-end fashion, allowing the anomaly detection module to tap on the supervised information available in the form of ratings. Thus, our model’s predictors enjoy the favourable generalization properties that come with being chosen from small function space (i.e., low-rank matrices), whilst exhibiting the robustness to outliers and flexibility that comes with deep learning methods. Furthermore, the anomaly scores themselves contain valuable qualitative information. Experiments on various real-life datasets demonstrate that our model outperforms standard matrix completion and other baselines, confirming the usefulness of the anomaly detection module.