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\section*{Matrix completion as a predictor}  \section*{Matrix completion} A dataset of peptide-MHC affinities for $n$ peptides and $a$ alleles may be thought of as a $n \times a$ matrix where peptide/allele pairs without measurements are considered missing values. Various heuristic or optimization-based algorithms have been developed to fill in these values.  We first investigated the performance of several matrix completion and imputation algorithms as a standalone solution to the peptide-MHC affinity prediction problem. The algorithms considered were:  \begin{itemize}  \item {\bf meanFill}: Replace each missing pMHC binding affinity with the mean affinity for that allele. This is a very simple imputation method which serves as a baseline against which other methods can be compared.  
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\item {\bf MICE}~\cite{Azur_2011}: Average multiple imputations generated using Gibbs sampling from the joint distribution of columns.   \end{itemize}  We found that MICE performed best.  \begin{table}[htbp]  \centering