Overlap Number of Balls Model-Agnostic CounterFactuals (ONB-MACF): A Data-Morphology-based Counterfactual Generation Method for Trustworthy Artificial Intelligence

TL;DR

The paper tackles trustworthy AI by addressing counterfactual explanations for tabular data. It introduces ONB-MACF, a model-agnostic method that uses data morphology and class-dependent balls to approximate decision boundaries and generate feasible, sparse counterfactuals by moving toward opposing-ball centers. The approach yields deterministic, distribution-consistent counterfactuals and semifactuals, with strong empirical support from quantitative benchmarks and qualitative audits across eight datasets. Overall, ONB-MACF demonstrates that geometry-inspired data coverings can enhance explainability and model auditing, with potential for extensions to interpretable/rule-based systems and ethics-focused evaluations.

Abstract

Explainable Artificial Intelligence (XAI) is a pivotal research domain aimed at understanding the operational mechanisms of AI systems, particularly those considered ``black boxes'' due to their complex, opaque nature. XAI seeks to make these AI systems more understandable and trustworthy, providing insight into their decision-making processes. By producing clear and comprehensible explanations, XAI enables users, practitioners, and stakeholders to trust a model's decisions. This work analyses the value of data morphology strategies in generating counterfactual explanations. It introduces the Overlap Number of Balls Model-Agnostic CounterFactuals (ONB-MACF) method, a model-agnostic counterfactual generator that leverages data morphology to estimate a model's decision boundaries. The ONB-MACF method constructs hyperspheres in the data space whose covered points share a class, mapping the decision boundary. Counterfactuals are then generated by incrementally adjusting an instance's attributes towards the nearest alternate-class hypersphere, crossing the decision boundary with minimal modifications. By design, the ONB-MACF method generates feasible and sparse counterfactuals that follow the data distribution. Our comprehensive benchmark from a double perspective (quantitative and qualitative) shows that the ONB-MACF method outperforms existing state-of-the-art counterfactual generation methods across multiple quality metrics on diverse tabular datasets. This supports our hypothesis, showcasing the potential of data-morphology-based explainability strategies for trustworthy AI.

Figures (6)

• Figure 1: Given a dataset (represented by points $A$ to $H$), a class coverage mapping is obtained for a given distance metric (i.e. Manhattan); then, for each instance whose counterfactual is requested ($P$), said instance is assigned to an appropriate ball from the coverage ($A$), which helps select the closest class boundary ($A-E$), and counterfactual candidates ($C_{i}$) are generated between the boundary and the projected centre of the chosen ball of opposing class.
• Figure 2: Example of the class coverage using balls generated with the Manhattan distance, where the data for each class are symbolised by circles and squares respectively. First, for all points (\ref{['ejbolasa']}), the balls are generated with their maximum radii that excludes instances of the opposing class (\ref{['ejbolasb']}); then, those including the most instances (those in thick lines) are iteratively selected until they are all covered (\ref{['ejbolasc']}).
• Figure 3: For an instance's ball association using balls generated with the Manhattan distance, the boundaries amongst balls are studied to select the most appropriate one for the studied instance. In this example, point P is inside the balls centred on A and E, and is associated to A since it falls on its side of the boundary against E.
• Figure 4: For an instance's candidate counterfactual generation with a chosen opposing ball in a dataset with no immutable nor discrete features, a first candidate $C_{0}$ is given at the intersection of the boundary between the instance P's associated ball and the chosen opposing ball E and the segment that goes from the instance to the centre of the selected opposing ball. If that candidate's class is the given instance's, subsequent candidates $C_{i}$ are generated in the said segment in intervals with decreasing length until the class changes or a check limit is reached (in which case the counterfactual would be E).
• Figure 5: Comparison of the best-performing methods for the "Adult" (\ref{['fig_adult']}), "COMPAS" (\ref{['fig_compas']}), "Give Me Some Credit" (\ref{['fig_give']}), "HELOC" (\ref{['fig_heloc']}), "Irish" (\ref{['fig_irish']}), "Saheart" (\ref{['fig_saheart']}), "Titanic" (\ref{['fig_titanic']}) and "Wine" (\ref{['fig_wine']}) datasets.

Theorems & Definitions (1)

• Definition 2.1