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<p>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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( n \ge 250 \)</EquationSource> </InlineEquation>) and missingness up to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(30\%\)</EquationSource> </InlineEquation>, whereas they are statistically unstable for small samples (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( n=100 \)</EquationSource> </InlineEquation>) or when missingness exceeds <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(50\%\)</EquationSource> </InlineEquation></p>

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Confidence intervals for Random Forest permutation importance with missing data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月11日

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  • Nico Föge,
  • Markus Pauly

摘要

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 \(50\%\)