Probabilistic Linear Explanations

The XAI community has studied a wide range of queries and scores for explaining predictions of ML models. From a data management perspective, this proliferation of explanation notions calls for declarative query languages in which such notions can be specified, combined, and analyzed uniformly. In this paper, we develop such a framework for Boolean models. We first revisit FOIL, an interpretability query language for black-box models, and show that it has two fundamental limitations: it cannot express central optimality-based explanation queries, and its evaluation problem over decision trees is hard for every level of the polynomial hierarchy. We then introduce ExplAIner, a query language based on FOIL with an extended vocabulary and a layered structure. We show that ExplAIner can express a broad family of explanation notions, including abductive, contrastive, feature-based, and distance-based queries. We also prove that the evaluation problem for each query in ExplAIner belongs to the Boolean hierarchy over every class of Boolean models for which some basic predicates can be evaluated in polynomial time. In particular, that property holds for deterministic and decomposable Boolean circuits. Finally, we introduce Opt-FOIL, an optimization-oriented fragment of ExplAIner for computing explanations that are minimal with respect to strict partial orders, and prove that its evaluation problem is in $\mathrm{FP}^{\mathrm{NP}}$ under the same tractability assumptions. These complexity results have a direct algorithmic consequence: a fixed ExplAIner query can be evaluated with a fixed number of calls to a SAT solver, while a notion of explanation specified in Opt-FOIL can be computed with a polynomial number of such calls. This is particularly relevant in formal XAI, where SAT solvers have been successfully used to compute explanations for several classes of ML models.

Despite the wide use of explainability techniques to attempt to understand the behavior of Artificial Intelligence (AI), the generated explanations may not always be reliable. An explanation can appear plausible to humans but fail to capture the internal reasoning of a model, particularly when dealing with complex tabular data. This paper studies the trustworthiness of local explainability techniques when applied to complex tabular classification tasks, considering evaluated metrics for three main properties: faithfulness to the model's predictions, robustness to input data variations, and complexity of the explanation itself. A benchmark was performed for Local Interpretable Model-Agnostic Explanations (LIME), Kernel SHapley Additive exPlanations (SHAP), and Feature Ablation techniques, across 32 datasets and different types of machine learning models. Model performance ranges were analyzed to identify two groups: consensus-correct, which are samples that all models predicted correctly, and consensus-wrong, samples that all models predicted incorrectly. The obtained results demonstrate that that the explanations are not always correlated with a model's predictive performance. Instead, dataset complexity and feature distributions seem to be the main factors affecting explanation quality and reliability.

We investigate the explanability properties of the recently proposed linear-min-max neural networks. At initialization, they can be interpreted as k-medoids with the infinity norm as a distance. Then, they are trained using subgradient descent to better fit the data. The model has been shown to be a universal approximator. Yet, we can trace the decision process because a single most activated neuron is responsible for the value of the output. Using this property, we designed a pixel fragility measure that determines whether changes to a single pixel may be responsible to a change in the classification output. Experiments on the PneumoniaMnist dataset show that this explanation for the output of the neural network compares favorably to SHAP and Integrated Gradient.