# _Applied Sciences_
## 1 Introduction  
Gradient boosted tree (GBT) models [1] remain the state-of-the-art for many \"shallow\" learning tasks that are based on structured, tabular data sets [2; 3; 4]. Such tasks are often still found in high-stakes decision making domains, such as medical decision making [5; 6; 7; 8], justice and law [9; 10]; financial services [11; 12; 13]; and defence and military intelligence [14]. In these and similar domains, there is a high burden of accountability for decision makers to explain the reasoning behind their decisions. This burden only increases with the introduction of machine learning (ML) into decision making processes [15]. So, the very high accuracy and ease of use of GBT models is not enough to encourage their adoption because GBT models also typify the \"black box\" problem of uninterpretability. Hence, research in interpretable machine learning (IML) and explainable artificial intelligence (XAI) has emerged to overcome these barriers to adoption. Deriving explanations from the complex structure of GBT models (as an ensemble of decision trees) has remained an open challenge. Gradient-based attribution methods that are used to explain deep learning (DL) models and neural networks are unsuitable here because the internal sub-units of a GBT model are non-parametric and non-differentiable decision nodes. The available IML and XAI methods have several disadvantages. IML methods can be used to facilitate the interpretation of a GBT model, as well as other types of decision tree ensemble, also known as decision forests (DFs). These methods generate a cascading rule list (CRL) as an inherently interpretable proxy model. First, a very large set of candidate classification rules (CRs) is generated. The defragTrees [16] and inTrees [17] methods achieve this by extracting all possible CRs from the decision trees in the DF. Bayesian rule lists (BRLs) [18] use a different approach, which is to mine the rules directly from the training data. For all three methods, the candidate set of CRs isthen merged or pruned using, e.g., some Bayesian formulation into the final CRL. One disadvantage with this approach is the very high computational and memory cost of exploring the combinatorial search space of candidate CRs. Another is imperfect fidelity, which means that the proxy does not always agree with the reference model's classification. This is a consequence of the proxy's simplification of the complex behaviour of the black box reference model. Disagreement between the two results in a failure to explain the reference model. Currently available XAI methods for explaining GBT are the so called model-agnostic methods. Methods include locally interpretable model-agnostic explanations (LIMEs) [19], Shapley additive explanations (SHAP) [20], local rule-based explanations (LORE) [21], and anchors [22]. These general purpose methods are said to explain any model. This flexibility is achieved by using a synthetic data set to probe the reference black box model and infer a relationship between its inputs and outputs. However, these methods are disadvantaged because there is no introspection of the reference model or target distribution, which is thought to be essential for reliable explanations [23; 24]. Furthermore, the explanations can exhibit variance because of the non-deterministic data generation [25; 26]. High variance results in dissimilar explanations for similar instances. They can also be fooled by adversarial examples [27]. Furthermore, the synthetic data place too much weight on rare and impossible instances [28; 29; 30]. Recent contributions [31; 32] present model-specific XAI approaches that probe DF internals and generate a single CR as an explanation. Thus, these newer methods overcome the combined disadvantages of prior work and have been shown to outperform the model-agnostic XAI methods and CRL-based IML methods on other classes of DF. Namely, the random forest [33] and AdaBoost [34] models. Hence, there still remains a gap in the literature for model-specific explanation methods that target GBT models.