Trading Complexity for Sparsity in Random Forest Explanations

Abstract

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 multiple 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 prime-implicant explanations taking the form of subset-minimal implicants of the random forest, we introduce majoritary reasons which are subset-minimal implicants of a strict majority of decision trees. For these abductive explanations, the tractability of the generation problem (finding one reason) and the optimization problem (finding one minimum-sized reason) are investigated. Unlike prime-implicant explanations, majoritary reasons may contain redundant features. However, in practice, prime-implicant explanations - 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. They are also significantly larger than minimum-sized majoritary reasons which can be approached using an anytime Partial MaxSAT algorithm.

Computing Abductive Explanations for Boosted Trees

“…Though this test can be achieved in polynomial time for some families of classifiers f (including decision trees) [22,15], it is intractable in general. Especially, it is coNP-hard when f is a random forest [2]. Similarly, when f is a boosted tree BT , we have: Proposition 1.…”

“…• coNP-hardness: it has been shown in [2] (Proposition 3) that deciding whether t is an abductive explanation for x given a random forest RF over Boolean attributes is coNPcomplete. Thus, it is enough to show that we can associate in polynomial time any random forest RF = {T 1 , .…”

“…have been considered in such a perspective. Thus, [8,23,2] show how to derive abductive explanations for random forests [5]. An abductive explanation for an instance given a classifier is a subset of the characteristics of the instance that is enough to justify how the instance has been classified.…”

“…Unlike[20], we do not require abductive explanations to be minimal w.r.t. set inclusion, in order to keep the concept distinct (and actually more general) than the one of sufficient reasons 2. Sufficient reasons are also known as prime-implicant explanations[38].…”

Logic-Based Explainability in Machine Learning

“…Different duality results have been obtained [158,160], which related different kinds of explanations. Practically efficient logic encodings have been devised for computing explanations for a number of families of classifiers [23,151,153,155,161,171], Compilation approaches for explainability have been studied in a number of recent works [83,84,86,88,281,282]. A number of computational complexity results, that cover the computing of one explanations but also other queries, have been proved [21,149,155,171,215].…”