Trading Complexity for Sparsity in Random Forest Explanations

Random forests have long been considered as powerful model ensembles in machine learning. By training multiple decision trees, whose diversity is fostered through data and feature subsampling, the resulting random forest can lead to more stable and reliable predictions than a single decision tree. This however comes at the cost of decreased interpretability: while decision trees are often easily interpretable, the predictions made by random forests are much more difficult to understand, as they involve a majority vote over hundreds of decision trees. In this paper, we examine different types of reasons that explain "why" an input instance is classified as positive or negative by a Boolean random forest. Notably, as an alternative to sufficient reasons taking the form of prime implicants of the random forest, we introduce majoritary reasons which are prime implicants of a strict majority of decision trees. For these different abductive explanations, the tractability of the generation problem (finding one reason) and the minimization problem (finding one shortest reason) are investigated. Experiments conducted on various datasets reveal the existence of a trade-off between runtime complexity and sparsity. Sufficient reasons - for which the identification problem is DP-complete - are slightly larger than majoritary reasons that can be generated using a simple linear- time greedy algorithm, and significantly larger than minimal majoritary reasons that can be approached using an anytime P ARTIAL M AX SAT algorithm.