Confidence intervals for Random Forest permutation importance with missing data

Abstract Random Forests are renowned for their predictive accuracy, but valid inference – particularly about permutation-based feature importances – remains challenging. Existing methods, such as Ishwaran et al.’s (2019) confidence intervals (CIs), are promising but assume complete feature observation. However, real-world data often contains missing values. In this paper, we investigate how common imputation techniques affect the validity of Random Forest permutation-importance CIs when data are incomplete. Through an extensive simulation and real-world benchmark study, we compare state-of-the-art imputation methods across various missing-data mechanisms and missing rates. Our results show that single-imputation strategies , when paired with naive variance estimators, lead to low CI coverage due to underestimation of imputation uncertainty. As a remedy, we adapt Rubin’s rule to aggregate feature-importance estimates and their variances over several imputed datasets and account for imputation uncertainty. Our numerical results indicate that the adjusted CIs achieve better nominal coverage for moderate sample sizes ( $$ n \ge 250 $$ ) and missingness up to $$30\%$$ , whereas they are statistically unstable for small samples ( $$ n=100 $$ ) or when missingness exceeds $$50\%$$