Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicity
This work is significant for users of machine learning models who need reliable and actionable counterfactual explanations, especially in scenarios with model multiplicity.
This paper addresses the unreliability of counterfactual explanations (CEs) in low-density data regions by proposing DensityFlow, a generative framework that constructs robust CEs by adhering to high-confidence data manifolds. DensityFlow achieves superior validity under model multiplicity and significantly reduces query costs compared to ensemble-based baselines.
Counterfactual explanations (CEs) are essential for actionable recourse, yet their reliability is often compromised in low-density regions, where classifiers exhibit high variance. Unlike existing methods that rely on expensive ensemble intersections to define stability, we propose \textit{DensityFlow}, a generative framework that constructs robust CEs by adhering to the high-confidence data manifold. Specifically, we model the counterfactual generation as continuous-time dynamics parameterized by Neural ODE, guided by a differentiable density score to actively avoid uncertain, low-density areas. This density score is learned via Noise Contrastive Estimation, effectively leveraging a $(K{+}1)$-way discriminator to estimate density ratios. For black-box settings, we introduce a local proxy distillation mechanism that aligns a lightweight surrogate with the target model strictly within the trajectory of CE generation, enabling efficient gradient-based optimization with minimal queries. Experiments demonstrate that \textit{DensityFlow} achieves superior validity under model multiplicity while significantly reducing query costs compared to ensemble-based baselines. Our implementation is available at https://github.com/G-AILab/DensityFlow.