Removing the influence of a group variable in high-dimensional predictive modelling

In many application areas, predictive models are used to support or make important decisions. There is increasing awareness that these models may contain spurious or otherwise undesirable correlations. Such correlations may arise from a variety of sources, including batch effects, systematic measurement errors or sampling bias. Without explicit adjustment, machine learning algorithms trained using these data can produce out-of-sample predictions which propagate these undesirable correlations. We propose a method to pre-process the training data, producing an adjusted dataset that is statistically independent of the nuisance variables with minimum information loss. We develop a conceptually simple approach for creating an adjusted dataset in high-dimensional settings based on a constrained form of matrix decomposition. The resulting dataset can then be used in any predictive algorithm with the guarantee that predictions will be statistically independent of the nuisance variables. We develop a scalable algorithm for implementing the method, along with theory support in the form of independence guarantees and optimality. The method is illustrated on some simulation examples and applied to two case studies: removing machine-specific correlations from brain scan data, and removing ethnicity information from a dataset used to predict recidivism. That the motivation for removing undesirable correlations is quite different in the two applications illustrates the broad applicability of our approach.