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Distributed Multi-Level Matrix Completion for Medical Databases

Gathering the information contained in the databases of several hospitals is a step toward personalized medical care as it increases the chances of finding similar patient profiles and therefore provinding them better treatment. However, there are technical (computations and storage issues) and social barriers (privacy concerns) to the aggregation of medical data. Both obstacles can be overcome by turning to distributed computations so that hospitals only share some intermediate results instead of the raw data. As it is often the case, the medical databases are incomplete. One aim of the project is to impute the data of one hospital using the data of the other hospitals. This could also be an incentive to encourage the hospitals to participate in the project. In this talk, we will describe a single imputation method for multi-level (hierarchical) data that can be used to impute both quantitative, categorical and mixed data. This method is based on multi-level simultaneous component analysis (MLSCA) which basically decomposes the variability in both a between and within (hospitals) variability and performs a SVD on each part. The imputation method can be seen as an extension of matrix completion methods. The methods and their distributed versions are implemented in an R package.