title: Do little interactions get lost in dark random forests?
abstract: BACKGROUND
  Random forests have often been claimed to uncover interaction effects. However, if and how interaction effects can be differentiated from marginal effects remains unclear. In extensive simulation studies, we investigate whether random forest variable importance measures capture or detect gene-gene interactions. With capturing interactions, we define the ability to identify a variable that acts through an interaction with another one, while detection is the ability to identify an interaction effect as such.
  
  
  RESULTS
  Of the single importance measures, the Gini importance captured interaction effects in most of the simulated scenarios, however, they were masked by marginal effects in other variables. With the permutation importance, the proportion of captured interactions was lower in all cases. Pairwise importance measures performed about equal, with a slight advantage for the joint variable importance method. However, the overall fraction of detected interactions was low. In almost all scenarios the detection fraction in a model with only marginal effects was larger than in a model with an interaction effect only.
  
  
  CONCLUSIONS
  Random forests are generally capable of capturing gene-gene interactions, but current variable importance measures are unable to detect them as interactions. In most of the cases, interactions are masked by marginal effects and interactions cannot be differentiated from marginal effects. Consequently, caution is warranted when claiming that random forests uncover interactions.
authors.affiliation: Institut für Medizinische Biometrie und Statistik, Universität zu Lübeck, Universitätsklinikum Schleswig-Holstein, Campus Lübeck, Ratzeburger Allee 160, Lübeck, 23562, Germany.
authors.forename: Marvin N
authors.initials: MN
authors.lastname: Wright
authors.affiliation: Institut für Medizinische Biometrie und Statistik, Universität zu Lübeck, Universitätsklinikum Schleswig-Holstein, Campus Lübeck, Ratzeburger Allee 160, Lübeck, 23562, Germany.|Zentrum für Klinische Studien, Universität zu Lübeck, Universitätsklinikum Schleswig-Holstein, Campus Lübeck, Lübeck, Germany.|School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa.
authors.forename: Andreas
authors.initials: A
authors.lastname: Ziegler
authors.affiliation: Institut für Medizinische Biometrie und Statistik, Universität zu Lübeck, Universitätsklinikum Schleswig-Holstein, Campus Lübeck, Ratzeburger Allee 160, Lübeck, 23562, Germany. inke.koenig@imbs.uni-luebeck.de.
authors.forename: Inke R
authors.initials: IR
authors.lastname: König
mesh_terms: D004843:Epistasis, Genetic; D015810:Linkage Disequilibrium; D008957:Models, Genetic; D020641:Polymorphism, Single Nucleotide
keywords: Epistasis; Gene-gene interactions; Random forests; Trees; Variable importance