Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential predictor variables vary in their scale of measurement or their number of categories. This is particularly important in genomics and computational biology, where predictors often include variables of different types, for example when predictors include both sequence data and continuous variables such as folding energy, or when amino acid sequence data show different numbers of categories. Simulation studies are presented illustrating that, when random forest variable importance measures are used with data of varying types, the results are misleading because suboptimal predictor variables may be artificially preferred in variable selection. The two mechanisms underlying this deficiency are biased variable selection in the individual classification trees used to build the random forest on one hand, and effects induced by bootstrap sampling with replacement on the other hand. We propose to employ an alternative implementation of random forests, that provides unbiased variable selection in the individual classification trees. When this method is applied using subsampling without replacement, the resulting variable importance measures can be used reliably for variable selection even in situations where the potential predictor variables vary in their scale of measurement or their number of categories. The usage of both random forest algorithms and their variable importance measures in the R system for statistical computing is illustrated and documented thoroughly in an application re-analyzing data from a study on RNA editing. Therefore the suggested method can be applied straightforwardly by scientists in bioinformatics research.

https://link.springer.com/content/pdf/10.1186%2F1471-2105-8-25.pdf

Bias in random forest variable importance measures: Illustrations, sources and a solution

Tree-based machine learning models such as random forests, decision trees and gradient boosted trees are popular nonlinear predictive models, yet comparatively little attention has been paid to explaining their predictions. Here we improve the interpretability of tree-based models through three main contributions. (1) A polynomial time algorithm to compute optimal explanations based on game theory. (2) A new type of explanation that directly measures local feature interaction effects. (3) A new set of tools for understanding global model structure based on combining many local explanations of each prediction. We apply these tools to three medical machine learning problems and show how combining many high-quality local explanations allows us to represent global structure while retaining local faithfulness to the original model. These tools enable us to (1) identify high-magnitude but low-frequency nonlinear mortality risk factors in the US population, (2) highlight distinct population subgroups with shared risk characteristics, (3) identify nonlinear interaction effects among risk factors for chronic kidney disease and (4) monitor a machine learning model deployed in a hospital by identifying which features are degrading the model’s performance over time. Given the popularity of tree-based machine learning models, these improvements to their interpretability have implications across a broad set of domains. Tree-based machine learning models are widely used in domains such as healthcare, finance and public services. The authors present an explanation method for trees that enables the computation of optimal local explanations for individual predictions, and demonstrate their method on three medical datasets.

/pdf/from-local-explanations-to-global-understanding-with-2a9bkpgseg.pdf

From Local Explanations to Global Understanding with Explainable AI for Trees.

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.

/pdf/conditional-variable-importance-for-random-forests-yw6yxv0jzu.pdf

Conditional variable importance for random forests

Recursive partitioning methods have become popular and widely used tools for nonparametric regression and classification in many scientific fields. Especially random forests, which can deal with large numbers of predictor variables even in the presence of complex interactions, have been applied successfully in genetics, clinical medicine, and bioinformatics within the past few years. High-dimensional problems are common not only in genetics, but also in some areas of psychological research, where only a few subjects can be measured because of time or cost constraints, yet a large amount of data is generated for each subject. Random forests have been shown to achieve a high prediction accuracy in such applications and to provide descriptive variable importance measures reflecting the impact of each variable in both main effects and interactions. The aim of this work is to introduce the principles of the standard recursive partitioning methods as well as recent methodological improvements, to illustrate their usage for low and high-dimensional data exploration, but also to point out limitations of the methods and potential pitfalls in their practical application. Application of the methods is illustrated with freely available implementations in the R system for statistical computing.

https://epub.ub.uni-muenchen.de/10589/1/partitioning.pdf

An Introduction to Recursive Partitioning: Rationale, Application and Characteristics of Classification and Regression Trees, Bagging and Random Forests

Following the identification of several disease-associated polymorphisms by genome-wide association (GWA) analysis, interest is now focusing on the detection of effects that, owing to their interaction with other genetic or environmental factors, might not be identified by using standard single-locus tests. In addition to increasing the power to detect associations, it is hoped that detecting interactions between loci will allow us to elucidate the biological and biochemical pathways that underpin disease. Here I provide a critical survey of the methods and related software packages currently used to detect the interactions between genetic loci that contribute to human genetic disease. I also discuss the difficulties in determining the biological relevance of statistical interactions.

/pdf/detecting-gene-gene-interactions-that-underlie-human-b4212oddbp.pdf

Detecting gene-gene interactions that underlie human diseases

Genome-wide association studies for complex diseases will produce genotypes on hundreds of thousands of single nucleotide polymorphisms (SNPs). A logical first approach to dealing with massive numbers of SNPs is to use some test to screen the SNPs, retaining only those that meet some criterion for futher study. For example, SNPs can be ranked by p-value, and those with the lowest p-values retained. When SNPs have large interaction effects but small marginal effects in a population, they are unlikely to be retained when univariate tests are used for screening. However, model-based screens that pre-specify interactions are impractical for data sets with thousands of SNPs. Random forest analysis is an alternative method that produces a single measure of importance for each predictor variable that takes into account interactions among variables without requiring model specification. Interactions increase the importance for the individual interacting variables, making them more likely to be given high importance relative to other variables. We test the performance of random forests as a screening procedure to identify small numbers of risk-associated SNPs from among large numbers of unassociated SNPs using complex disease models with up to 32 loci, incorporating both genetic heterogeneity and multi-locus interaction. Keeping other factors constant, if risk SNPs interact, the random forest importance measure significantly outperforms the Fisher Exact test as a screening tool. As the number of interacting SNPs increases, the improvement in performance of random forest analysis relative to Fisher Exact test for screening also increases. Random forests perform similarly to the univariate Fisher Exact test as a screening tool when SNPs in the analysis do not interact. In the context of large-scale genetic association studies where unknown interactions exist among true risk-associated SNPs or SNPs and environmental covariates, screening SNPs using random forest analyses can significantly reduce the number of SNPs that need to be retained for further study compared to standard univariate screening methods.

/pdf/screening-large-scale-association-study-data-exploiting-450j6joiim.pdf

L Brooke Hayward

Papers

Screening large-scale association study data: exploiting interactions using random forests