Predicting the binding affinity between MHC proteins and their peptide ligands is a key problem in computational immunology. State of the art performance is currently achieved by the allele-specific predictor NetMHC and the pan-allele predictor NetMHCpan, both of which are ensembles of shallow neural networks. We explore an intermediate between allele-specific and pan-allele prediction: training allele-specific predictors with synthetic samples generated by imputation of the peptide-MHC affinity matrix. We find that the imputation strategy is useful on alleles with very little training data. We have implemented our predictor as an open-source software package called MHCflurry and show that MHCflurry achieves competitive performance to NetMHC and NetMHCpan.