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Open Access Highly Accessed Methodology article

Conditional variable importance for random forests

Carolin Strobl1*, Anne-Laure Boulesteix2, Thomas Kneib1, Thomas Augustin1 and Achim Zeileis3

Author affiliations

1 Department of Statistics, Ludwig-Maximilians-Universität Munchen, Ludwigstraße 33, D-80539 München, Germany

2 Sylvia Lawry Centre for Multiple Sclerosis Research, Hohenlindener Straße 1, D-81677 München, Germany

3 Department of Statistics and Mathematics, Wirtschaftsuniversität Wien, Augasse 2 – 6, A-1090 Wien, Austria

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Citation and License

BMC Bioinformatics 2008, 9:307  doi:10.1186/1471-2105-9-307

Published: 11 July 2008



Random forests are becoming increasingly popular in many scientific fields because they can cope with "small n large p" problems, complex interactions and even highly correlated predictor variables. Their variable importance measures have recently been suggested as screening tools for, e.g., gene expression studies. However, these variable importance measures show a bias towards correlated predictor variables.


We identify two mechanisms responsible for this finding: (i) A preference for the selection of correlated predictors in the tree building process and (ii) an additional advantage for correlated predictor variables induced by the unconditional permutation scheme that is employed in the computation of the variable importance measure. Based on these considerations we develop a new, conditional permutation scheme for the computation of the variable importance measure.


The resulting conditional variable importance reflects the true impact of each predictor variable more reliably than the original marginal approach.