Navigating Explanatory Multiverse Through Counterfactual Path Geometry

Counterfactual explanations are the de facto standard when tasked with interpreting decisions of (opaque) predictive models. Their generation is often subject to technical and domain-specific constraints that aim to maximise their real-life utility. In addition to considering desiderata pertaining to the counterfactual instance itself, guaranteeing existence of a viable path connecting it with the factual data point has recently gained relevance. While current explainability approaches ensure that the steps of such a journey as well as its destination adhere to selected constraints, they neglect the multiplicity of these counterfactual paths. To address this shortcoming we introduce the novel concept of explanatory multiverse that encompasses all the possible counterfactual journeys. We define it using vector spaces, showing how to navigate, reason about and compare the geometry of counterfactual trajectories found within it. To this end, we overview their spatial properties -- such as affinity, branching, divergence and possible future convergence -- and propose an all-in-one metric, called opportunity potential, to quantify them. Notably, the explanatory process offered by our method grants explainees more agency by allowing them to select counterfactuals not only based on their absolute differences but also according to the properties of their connecting paths. To demonstrate real-life flexibility, benefit and efficacy of explanatory multiverse we propose its graph-based implementation, which we use for qualitative and quantitative evaluation on six tabular and image data sets.