Source-linked AI summary
FACE: Feasible and Actionable Counterfactual Explanations
Rafael Poyiadzi, Kacper Sokol, Raul Santos-Rodriguez, Tijl De Bie, Peter Flach
TL;DR
Existing counterfactual methods emphasize small changes toward a desired outcome but may propose atypical targets or transformations without feasible paths. FACE addresses this gap by using density-weighted shortest paths, producing distributionally coherent, actionable explanations that can be tailored to users.
Problem
The closest-possible-world approach may generate counterfactuals that are not representative of the data distribution or lack feasible paths from the current state.
Method
FACE finds counterfactuals using shortest path distances based on density-weighted metrics and supports user-imposed feasibility and classifier-confidence constraints.
Results
FACE produces explanations from dense regions connected to the original instance by high-density paths.
Takeaways & Limitations
The resulting explanations are coherent with the underlying data distribution and can be tailored by customizing feasible paths of change.
Takeaways & Limitations
The theory holds only for continuous distributions satisfying the stated requirements, although the approach can still be used with discrete features.
Abstract
from arXiv · showhide
Work in Counterfactual Explanations tends to focus on the principle of "the closest possible world" that identifies small changes leading to the desired outcome. In this paper we argue that while this approach might initially seem intuitively appealing it exhibits shortcomings not addressed in the current literature. First, a counterfactual example generated by the state-of-the-art systems is not necessarily representative of the underlying data distribution, and may therefore prescribe unachievable goals(e.g., an unsuccessful life insurance applicant with severe disability may be advised to do more sports). Secondly, the counterfactuals may not be based on a "feasible path" between the current state of the subject and the suggested one, making actionable recourse infeasible (e.g., low-skilled unsuccessful mortgage applicants may be told to double their salary, which may be hard without first increasing their skill level). These two shortcomings may render counterfactual explanations impractical and sometimes outright offensive. To address these two major flaws, first of all, we propose a new line of Counterfactual Explanations research aimed at providing actionable and feasible paths to transform a selected instance into one that meets a certain goal. Secondly, we propose FACE: an algorithmically sound way of uncovering these "feasible paths" based on the shortest path distances defined via density-weighted metrics. Our approach generates counterfactuals that are coherent with the underlying data distribution and supported by the "feasible paths" of change, which are achievable and can be tailored to the problem at hand.
1 INTRODUCTION
Counterfactual explanations answer what someone could change to obtain a desired outcome, but nearest-world methods may suggest distributionally atypical or impractical changes. FACE instead targets counterfactuals in dense regions connected to the original instance by feasible paths.
- Counterfactual explanations ask what must change for a desired outcome, complementing explanations of why a decision occurred.
- The closest-possible-world principle can produce counterfactuals outside the underlying data distribution and prescribe unachievable goals.Points A and B in Figure 1 are close under the l2-norm but lie in low-density regions with no similar precedents.
- Counterfactuals can also lack a feasible path from the initial instance, making actionable recourse impractical.Figure 1 contrasts C, which is closer, with D, which is connected to the original instance by a high-density path.
- FACE introduces feasible and actionable counterfactual explanations that respect the data distribution and connect targets to the explained instance through high-density paths.The method uses shortest path distances defined via density-weighted metrics and allows paths to be tailored to the problem.
2 COUNTERFACTUAL EXPLANATIONS
The paper argues that practical counterfactual explanations must account for the target instance, the transformation path, and the density of that path. It therefore proposes feasibility and actionability as explicit objectives alongside achieving the desired class.
- Target counterfactuals may be outliers in low-density regions, making them poor explanations and potentially harmful advice.
- High prediction uncertainty can create delayed-impact problems even when implementing a proposed counterfactual initially yields acceptance.
- Existing counterfactual desiderata overlook whether the suggested transformation is feasible for the explainee to undertake.A rejected loan applicant may disregard advice conditioned on becoming 10 years younger.
- The paper adds three objectives: feasible target points, continuous feasible paths, and relatively short, high-density paths.
3 FEASIBLE COUNTERFACTUALS
FACE models counterfactual recourse as density-aware paths through a graph of observed data, balancing path length, density, feasibility, and prediction confidence. Users can impose domain-specific transition constraints and customize graph construction or costs.
- Background: The f-geodesic is the path with minimum f-length between two instances.For density-dependent f, the path length is defined by a line integral and approximated through graph weights.
- Graph construction: FACE supports KDE, k-NN, and ϵ-graph constructions, using zero edge weight when the required proximity condition is not satisfied.KDE estimates density directly, while k-NN and ϵ-graph approaches can avoid density estimation.
- Method: FACE approximates density-weighted path distances on a finite graph and minimizes them with a shortest-path algorithm.The graph connects nearby training instances, with edge weights encoding distance and density; Dijkstra’s algorithm is used for path search.
- Constraints: Users can constrain candidate targets by prediction confidence and density thresholds, custom weights, and feasibility conditions on transitions.Domain knowledge such as immutable or directionally changing features is encoded in the conditions function.
- Efficiency: Reducing the number of candidate instances can improve speed but creates a trade-off with counterfactual accuracy.Random subsampling and Maximum Mean Discrepancy are suggested as alternatives related to prototype selection.
- Personalization: Personalized restrictions can remove edges from a stored base graph, whereas a custom cost function requires rebuilding the graph.The theoretical guarantees assume continuous distributions, although the approach can still be used with discrete features.
4 EXPERIMENTS
The experiments evaluate FACE on a toy dataset with three graph constructions and on MNIST digit transformations. On MNIST, FACE produces a smooth path transforming zeros into eights.
- Experimental design: FACE is evaluated on a toy dataset and MNIST to examine graph construction and meaningful digit transformations.The toy experiment compares KDE, ϵ-graph, and k-NN approaches; MNIST evaluates paths from zero to eight.
- Synthetic data: The toy experiments use a two-hidden-layer ReLU neural network and FACE weights w(z) = −log(z) with l2 distance.Figures 2–4 present no, good, and bad counterfactual cases for KDE, ϵ-graph, and k-NN.
- MNIST: With k = 50, FACE transforms MNIST zeros smoothly through intermediate zeros until reaching the target class eight.The reported path runs from the starting image to the final counterfactual.
5 RELATED WORK
FACE is positioned against prior counterfactual methods by combining model-agnostic generation with feasible, actionable changes supported by data structure and transformation paths.
- Existing counterfactual methods: Wachter et al. formulate counterfactual generation around distance to the current instance and achieving a desired classifier outcome.Their approach uses iterative optimization and can employ an l1-norm penalty to induce sparse changes.
- Existing counterfactual methods: Ustun et al. provide integer programming tools for actionable recourse in linear classification, while Russell uses mixed-polytopes to preserve data structure.Russell’s formulation handles mixed data types and ranks diverse counterfactuals by l1-distance.
- FACE comparisons: FACE generates five shortest paths using graph edge weights computed by KDE, e-graphs, or k-NN graphs, subject to prediction and graph-specific constraints.The figures compare KDE targets with prediction and density thresholds, e-graph targets with prediction thresholds, and k-NN settings with different k and epsilon values.
- FACE comparisons: Figure 5 contrasts FACE’s desired properties with counterfactuals generated by Wachter et al., parameterized by penalty p and classification threshold t.The caption states that these counterfactuals do not comply with the properties described in Section 2.
- Existing counterfactual methods: Waa et al. generate decision-tree counterfactuals from locally trained one-vs-rest trees and disjoint rules leading to a target class.The approach is specialized to decision-tree settings.
- FACE comparisons: FACE differs from the compared approaches by supporting discrete-feature restrictions, remaining model-agnostic, and producing feasible and actionable counterfactual explanations.These distinctions are stated as the paper’s comparison across Wachter, Ustun, Russell, and Waa.
6 SUMMARY AND FUTURE WORK
The paper identifies shortcomings in popular counterfactual explanation methods and proposes FACE to account for the nature and feasibility of proposed changes. Future work will evaluate FACE on dynamic real-world datasets and compare its suggestions with true changes.
- Summary: FACE addresses shortcomings of popular counterfactual explanation methods by accounting for whether proposed changes are feasible and actionable.The paper presents this as the method’s central contribution.
- Future work: Future work will evaluate FACE on real-world datasets of dynamic nature and examine how closely its counterfactuals match true change.These directions are explicitly identified by the authors.