@phdthesis{Lehner2025, author = {Lehner, Constanze}, title = {Three Essays on the Interpretability of Random Forests: Methods, Insights, and Innovations}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus4-18608}, school = {Universit{\"a}t Passau}, pages = {126 Seiten}, year = {2025}, abstract = {This thesis examines the interpretability of random forests in three essays, focusing on the discussion of established methods, the presentation of new insights and the provision of innovations. The research aims to bridge the gap between traditional statistical methods and random forests, a data-driven machine learning algorithm, by investigating the ability of random forests to adequately model theoretical concepts compared to parametric methods and developing a new approach for statistical hypothesis testing. The results have implications for various areas of research in which interpretability is crucial for applications. The next three paragraphs summarize the studies presented in this thesis. The ability of random forests to automatically model interactions without the need for pre-specification is mentioned prominently in many articles and book chapters. Promising empirical results from early work on random forests have substantiated this property, which has led to an increasing popularity of using random forests in the presence of interactions as an alternative to traditional parametric methods. This study reviews the literature of the last 20 years on random forests and interactions. We explore the discussion from its origin in the decision tree literature to early applications of random forests and current research. We identify key research areas and illustrate random forest applications to highlight similarities and differences between disciplines. We also provide a critical examination of the arguments in favor of random forests being able to model interactions automatically. Since the term ``interaction'' is associated with different theoretical concepts, we explain and illustrate the definition of interaction for each research area. The variable importance of random forests is an easy-to-understand metric that intends to make the predictions of random forests more transparent by assessing the contribution of each covariate to the prediction of the response. However, due to its data-driven nature, the variable importance of random forests may over- or underestimate the importance of a covariate, so that the role of the covariate in the underlying data generating process is not correctly reflected. We present an example of underestimation of importance in the case of interacting covariates. We define an interaction in terms of effect modification, which assumes that the effect of one covariate on the response is modified by values of another covariate. We show that the variable importance of random forests is influenced by the interaction form and the measurement scale of the interacting covariates, so that in some cases the importance of one or even both interacting covariates is underestimated. We illustrate how the split decisions of random forests affect the variable importance values of the interacting covariates. Variable importance estimates the contribution of a covariate to the performance of a predictive algorithm. Defined as the increase in loss after the random permutation of a covariate, permutation variable importance makes it possible to rank the covariates by importance, but in the absence of a threshold, the distinction between important and unimportant covariates is inherently arbitrary. We show that recent approaches of non-parametric permutation tests for variable importance exceed their nominal type I error level for mutually dependent covariates. As an alternative we propose a combined variable importance estimate on a sequence of permutations and employ a computationally more efficient bootstrap to derive the respective null distribution and \$p\$-values. The proposed test can be applied to any predictive algorithm and is remarkably fast. We investigate the control of type I error level and the power of the proposed variable importance test in simulation studies. Even for mutually dependent covariates, our test is conservative and provides power comparable to recent advances in non-parametric permutation tests of variable importance. This study was conducted in collaboration with Matthias Wild.}, language = {en} }