Correlation and variable importance in random forests

Baptiste Gregorutti (1) , Bertrand Michel (1) , Philippe Saint-Pierre (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

This paper is about variable selection with random forests algorithm in presence of correlated predictors. In high-dimensional regression or classification frameworks, variable selection is a difficult task, that becomes even more challenging in the presence of highly correlated predictors. Firstly we provide a theoretical study of the permutation importance measure for an additive regression model. This allows us to describe how the correlation between predictors impacts the permutation importance. Our results motivate the use of the Recursive Feature Elimination (RFE) algorithm for variable selection in this context. This algorithm recursively eliminates the variables using permutation importance measure as a ranking criterion. Next various simulation experiments illustrate the efficiency of the RFE algorithm for selecting a small number of variables together with a good prediction error. Finally, this selection algorithm is tested on a real life dataset from aviation safety where the flight data recorders are analysed for the prediction of a dangerous event.

Mots clés: Random forests; Supervised learning; Variable importance; Variable selection

Domaines: Méthodologie [stat.ME]

Baptiste Gregorutti, Bertrand Michel, Philippe Saint-Pierre. Correlation and variable importance in random forests. 2013. ⟨hal-00879978⟩