Regularized Optimal Transport of Covariates and Outcomes in Data Recoding

When databases are constructed from heterogeneous sources, it is not unusual that different encodings are used for the same outcome. In such case, it is necessary to recode the outcome variable before merging two databases. The method proposed for the recoding is an application of optimal transportation where we search for a bijective mapping between the distributions of such variable in two databases. In this article, we build upon the work by Garés et al., where they transport the distributions of categorical outcomes assuming that they are distributed equally in the two databases. Here, we extend the scope of the model to treat all the situations where the covariates explain the outcomes similarly in the two databases. In particular, we do not require that the outcomes be distributed equally. For this, we propose a model where joint distributions of outcomes and covariates are transported. We also propose to enrich the model by relaxing the constraints on marginal distributions and adding an L1 regularization term. The performances of the models are evaluated in a simulation study, and they are applied to a real dataset. The code used in the computational assessment and in the simulation of test cases is publicly available on Github repository: https://github.com/otrecoding/OTRecod.jl.