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Random forests have long been considered as powerful model ensembles inmachine learning. By training multiple decision trees, whose diversity isfostered through data and feature subsampling, the resulting random forest canlead to more stable and reliable predictions than a single decision tree. Thishowever comes at the cost of decreased interpretability: while decision treesare often easily interpretable, the predictions made by random forests are muchmore difficult to understand, as they involve a majority vote over hundreds ofdecision trees. In this paper, we examine different types of reasons thatexplain "why" an input instance is classified as positive or negative by aBoolean random forest. Notably, as an alternative to sufficient reasons takingthe form of prime implicants of the random forest, we introduce majoritaryreasons which are prime implicants of a strict majority of decision trees. Forthese different abductive explanations, the tractability of the generationproblem (finding one reason) and the minimization problem (finding one shortestreason) are investigated. Experiments conducted on various datasets reveal theexistence of a trade-off between runtime complexity and sparsity. Sufficientreasons - for which the identification problem is DP-complete - are slightlylarger than majoritary reasons that can be generated using a simple linear-time greedy algorithm, and significantly larger than minimal majoritary reasonsthat can be approached using an anytime P ARTIAL M AX SAT algorithm.

Trading Complexity for Sparsity in Random Forest Explanations