On Tackling Explanation Redundancy in Decision Trees

Abstract

Decision trees (DTs) epitomize the ideal of interpretability of machine learning (ML) models. The interpretability of decision trees motivates explainability approaches by so-called intrinsic interpretability, and it is at the core of recent proposals for applying interpretable ML models in high-risk applications. The belief in DT interpretability is justified by the fact that explanations for DT predictions are generally expected to be succinct. Indeed, in the case of DTs, explanations correspond to DT paths. Since decision trees are ideally shallow, and so paths contain far fewer features than the total number of features, explanations in DTs are expected to be succinct, and hence interpretable. This paper offers both theoretical and experimental arguments demonstrating that, as long as interpretability of decision trees equates with succinctness of explanations, then decision trees ought not be deemed interpretable. The paper introduces logically rigorous path explanations and path explanation redundancy, and proves that there exist functions for which decision trees must exhibit paths with explanation redundancy that is arbitrarily larger than the actual path explanation. The paper also proves that only a very restricted class of functions can be represented with DTs that exhibit no explanation redundancy. In addition, the paper includes experimental results substantiating that path explanation redundancy is observed ubiquitously in decision trees, including those obtained using different tree learning algorithms, but also in a wide range of publicly available decision trees. The paper also proposes polynomial-time algorithms for eliminating path explanation redundancy, which in practice require negligible time to compute. Thus, these algorithms serve to indirectly attain irreducible, and so succinct, explanations for decision trees. Furthermore, the paper includes novel results related with duality and enumeration of explanations, based on using SAT solvers as witness-producing NP-oracles.

Logic-Based Explainability in Machine Learning

“…Example 7 illustrates important limitations of DTs in terms of interpretability, and justifies recent work on explaining DTs [166][167][168]. More importantly, it has been shown that the redundancy in tree paths (i.e.…”

“…Some other authors propose the use of interpretable models as the explanation itself [232,267,268]. There is by now mounting evidence [149,155,166,167,214] that even these so-called interpretable models ought to be explained with the methods described in this paper 4 .…”

“…(The interested reader is referred to a standard reference on the computational complexity [19].) 4 More importantly, the growing evidence on the need to explain "interpretable" models [149,155,167,167,214] justifies wondering, in hindsight, about the practical relevancy of learning (quasi-)optimal interpretable models [4, 5, 8, 14, 15, 27, 28, 44, 45, 66, 90, 91, 121-123, 145, 146, 154, 162, 176, 197, 204, 213, 225, 238, 242, 243, 247, 269, 275, 279, 304-307, 310, 311, 314, 316, 321, 322].…”

“…9, Page 206]; hence decision trees have been applied to a wide range of domains, including the medical domain [298]. Unfortunately, recent results [167] demonstrate that decision trees can hardly be deemed interpretable, at least as long as interpretability correlates with succinctness of explanations. The bottom line is that even interpretable ML models should be explained.…”

“…Among these, several results are significant. It has been shown that computing one explanation is tractable for a number of classifiers [72,86,148,149,166,167,214,215]. Different duality results have been obtained [158,160], which related different kinds of explanations.…”