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The primary difference between NetMHC and NetMHCpan is that the former is an ``allele-specific'' method which trains a separate predictor for each allele's binding dataset, whereas the latter is a ``pan-allele'' method whose inputs are vector encodings of both the peptide and a subset of MHC molecule's primary sequence. The conventional wisdom is that NetMHC performs better on alleles with many assayed ligands whereas NetMHCpan is superior for less well-characterized alleles~\cite{Gfeller_2016}.  In this paper we explore the space between ``allele-specific'' {\it allele-specific}  and ``pan-allele'' {\it pan-allele}  prediction by imputing the unobserved values of peptide-MHC affinities for which we have no measurements and using these imputed values for pre-training of allele-specific binding predictors.