UAFS: Uncertainty-Aware Feature Selection for Problems with Missing Data

Abstract: Missing data are a concern in many real world data sets and imputation methods are often needed to estimate the values of missing data, but data sets with excessive missingness and high dimensionality challenge most approaches to imputation. Here we show that appropriate feature selection can be an effective preprocessing step for imputation, allowing for more accurate imputation and subsequent model predictions. The key feature of this preprocessing is that it incorporates uncertainty: by accounting for uncertainty due to missingness when selecting features we can reduce the degree of missingness while also limiting the number of uninformative features being used to make predictive models. We introduce a method to perform uncertainty-aware feature selection (UAFS), provide a theoretical motivation, and test UAFS on both real and synthetic problems, demonstrating that across a variety of data sets and levels of missingness we can improve the accuracy of imputations. Improved imputation due to UAFS also results in improved prediction accuracy when performing supervised learning using these imputed data sets. Our UAFS method is general and can be fruitfully coupled with a variety of imputation methods.