Counterfactual Maps: What They Are and How to Find Them

TL;DR

This paper introduces counterfactual maps, an exact and efficient method for generating optimal counterfactual explanations for tree ensemble models using a geometric approach and KD-trees.

Contribution

It presents a novel geometric framework and an amortized algorithm for exact counterfactual search in tree ensembles, significantly improving speed and optimality guarantees.

Findings

Achieves millisecond-level latency for counterfactual queries.

Outperforms existing methods in speed by orders of magnitude.

Provides globally optimal counterfactual explanations.

Abstract

Counterfactual explanations are a central tool in interpretable machine learning, yet computing them exactly for complex models remains challenging. For tree ensembles, predictions are piecewise constant over a large collection of axis-aligned hyperrectangles, implying that an optimal counterfactual for a point corresponds to its projection onto the nearest rectangle with an alternative label under a chosen metric. Existing methods largely overlook this geometric structure, relying either on heuristics with no optimality guarantees or on mixed-integer programming formulations that do not scale to interactive use. In this work, we revisit counterfactual generation through the lens of nearest-region search and introduce counterfactual maps, a global representation of recourse for tree ensembles. Leveraging the fact that any tree ensemble can be compressed into an equivalent partition of labeled hyperrectangles, we cast counterfactual search as the problem of identifying the generalized Voronoi cell associated with the nearest rectangle of an alternative label. This leads to an exact, amortized algorithm based on volumetric k-dimensional (KD) trees, which performs branch-and-bound nearest-region queries with explicit optimality certificates and sublinear average query time after a one-time preprocessing phase. Our experimental analyses on several real datasets drawn from high-stakes application domains show that this approach delivers globally optimal counterfactual explanations with millisecond-level latency, achieving query times that are orders of magnitude faster than existing exact, cold-start optimization methods.