Navigating Explanatory Multiverse Through Counterfactual Path Geometry

Counterfactual explanations are the de facto standard when attempting to interpret the decisions of opaque predictive models. Their generation is often subject to algorithmic and domain-specific constraints -- such as density-based feasibility for the former, and attribute (im)mutability or directionality of change for the latter -- that aim to maximise their real-life practicality. In addition to desiderata with respect to the counterfactual instance itself, the existence of a viable path connecting it with the factual data point, known as algorithmic recourse, has become an important technical consideration. While both of these requirements ensure that the steps of the journey as well as its destination are admissible, current literature does not deal with the multiplicity of such counterfactual paths. To address this shortcoming we introduce the novel concept of explanatory multiverse that encompasses all the possible counterfactual journeys, and show how to navigate, reason about and compare the geometry of these paths -- their affinity, branching, divergence and possible future convergence -- with two methods: vector spaces and graphs. Implementing this (interactive) explanatory process grants explainees more agency by allowing them to select counterfactuals based on the properties of the journey leading to them in addition to their absolute differences.