binomialRF: Scalable Feature Selection and Screening for Random Forests to Identify Biomarkers and Their Interactions

Background Feature selection is becoming increasingly important in machine learning as users want more interpretation and post-hoc analyses. However, existing feature selection techniques in random forests are computationally intensive and high RAM memory requirements requiring specialized (uncommon) high throughput infrastructures. In bioinformatics, random forest classifiers are widely used as it is a flexible, self-regulating and self-contained machine learning algorithm that is robust to the “predictors(features) P ≫ subjects N” problem with minimal tuning parameters. The current feature selection options are used extensively for biomarker detection and discovery; however, they are limited to variants of permutation tests or heuristic rankings with arbitrary cutoffs. In this work, we propose a novel paradigm using the binomial framework for feature selection in random forests, binomialRF, which is designed to produce significance measures devoid of expensive and uninterpretable permutation tests. Furthermore, it offers a highly flexible framework for efficiently identifying and ranking multi-way interactions via dynamic tree programming.

Methods We propose a novel and scalable feature selection technique that exploits the tree structure in the random forest, treats each tree as a binomial stochastic process, and determines feature significance by conducting a one-sided binomial exact test to determine if a feature was detected more often than expected by random chance. Since each tree is an independent and identically distributed random sample in a binomial process (from the perspective of choosing a splitting variable in the root node), the test statistic is constructed based on the frequency of a feature being selected (each tree is a Bernoulli trial for selecting a feature), and then the features are ranked based on the observed test statistics, its resulting nominal p-values, and its multiplicity-adjusted q-values. Furthermore, the binomialRF framework provides a general selection framework to identify 2-way, 3-way, and K-way interactions by generalizing the test statistic to count sub-trees in the random forest using dynamic tree programming.

Results In simulation studies, the binomialRF algorithm performs competitively with respect to the state of the art in terms of classification accuracy, true model coverage, and controlling for false selection in identifying main effects while attaining substantial computational performance gains (between 30 to 600 times faster in high dimensional settings than the state of the art). In addition, extending the binomialRF using model averaging identified the true model on average with greater accuracy (>20% improvement in reducing false positive feature selection at high dimensions while maximizing true model coverage) and attained greater classification accuracy (between 4-9% improvement across all techniques) without sacrificing computational speed (2^nd fastest performance after binomialRF). In addition, the framework easily scales and extends to identifying 2-way and K-way interactions (i) without additional memory requirements (only requires storing original predictor matrix), and (ii) with minimal additional computational complexity cost due to efficient dynamic tree programming interaction searches. The algorithm was validated in a case study to predict bronchospasm-related hospitalization from blood transcriptomes where the binomialRF algorithm correctly identified the previously published relevant physiological pathways, presented comparable classification accuracy in a validation set, and extended previous work in this area by looking at pathway-pathway interaction.

Conclusion The proposed binomialRF proposes a novel and efficient feature selection method devoid of permutation tests – that scales linearly in the number of trees, with minimal computational complexity, thus outperforming alternate conventional methods from a computational perspective while attaining competitive model selection and classification accuracies and enabling computations on common of cost-effective high throughput infrastructures. Furthermore, the binomialRF model averaging framework greatly improves the accuracy of the feature predictions, controlling for false selection and substantially improving model and classification accuracy. Validated in numerical studies and retrospectively in a clinical trial (case study), the binomialRF paradigm offers a binomial framework to detect feature significance and easily extends to search for K-way interactions in a linear fashion, reducing a known non-polynomial time exploration to linear approximations.

The binomialRF R package is freely available on GitHub and has been submitted to BioConductor, with all associated documentations and help files.

Github: https://github.com/SamirRachidZaim/binomialRF

BioConductor: binomialRF