FCx: An algorithm for finding Feasible Counterfactual Explanations
Authors: Kleopatra Markou, Vana Kalogeraki, Dimitrios Gunopulos
Organizations: National and Kapodistrian University of Athens, Department of Informatics and Telecommunications, Greece · Athens University of Economics and Business, Department of Informatics, Greece
Counterfactual (CF) explanations identify changes that alter an input's classification. While existing methods produce realistic and low-cost CFs, they often fail to ensure feasibility, by suggesting non-constructive modifications or incompatible with future changes (e.g., changing an individual's race to secure a job offer). We introduce a refinement of CF explanations that explicitly enforces feasibility. Our approach is the first to efficiently generate CFs that are realistic, low-cost and feasible. We accommodate both hard feasible constraints, specified by domain knowledge users, and soft feasible constraints, inferred automatically via causal inference from the dataset. Our method, Feasible Counterfactual Explanations (FCx), is based on a modified Variational Autoencoder (VAE) optimized with a multi-factor loss function. We measure the cost of a change based on the absolute change in values (proximity) as well as the number of features changed (sparsity) while realism is measured based on the LOF for density estimation, guaranteeing that CFs reside in densely populated regions. Extensive experiments on four public datasets show that our approach matches state-of-the-art performance across multiple metrics while guaranteeing feasibility.
The increasing use of machine learning algorithms in social applications has raised concerns about fairness and transparency, leading to the development of counterfactual explanations. These explanations supports individuals to understand and potentially alter unfavorable decisions in areas such as loan applications, job selections, and more, by providing actionable changes to input features that would lead to a desired outcome. Existing methods often struggle to balance feasibility, plausibility, and computational efficiency. To address this, we introduce P2CE, an algorithm for generating plausible Pareto-optimal counterfactual explanations, offering users a diverse set of optimal trade-offs between different notions of feasibility. P2CE employs an auxiliary isolation forest outlier detector to ensure that explanations are in accordance with the data distribution and leverages SHAP values to obtain optimal results with short computing times, regardless of the underlying model. Our algorithm was empirically evaluated on three datasets, demonstrating superior performance in terms of both solution quality and computational efficiency compared to related techniques.
Arthur Hendricks Mendes de Oliveira, Giovani Valdrighi, Marcos Medeiros Raimundo
Counterfactual explanations (CFEs) are essential for interpreting black-box models, yet they often become invalid when models are slightly changed. Existing methods for generating robust CFEs are often limited to specific types of models, require costly tuning, or inflexible robustness controls. We propose a novel approach that jointly models the data distribution and the space of plausible model decisions to ensure robustness to model changes. Using a probabilistic consensus over a model ensemble, we train a conditional normalizing flow that captures the data density under varying levels of classifier agreement. At inference time, a single interpretable parameter controls the robustness level; it specifies the minimum fraction of models that should agree on the target class without retraining the generative model. Our method effectively pushes CFEs toward regions that are both plausible and stable across model changes. Experimental results demonstrate that our approach achieves superior empirical robustness while also maintaining good performance across other evaluation measures.
Counterfactual explanations (CE) explain model decisions by identifying input modifications that lead to different predictions. Most existing methods operate at the instance level. Distributional Counterfactual Explanations (DCE) extend this setting by optimizing an optimal transport objective that balances proximity to a factual input distribution and alignment to a target output distribution, with statistical certification via chance constrained bounds. However, DCE relies on gradient based optimization, while many real-world tabular pipelines are dominated by non-differentiable models. We propose DISCOVER, a model-agnostic solver for distributional counterfactual explanations. DISCOVER preserves the original DCE objective and certification while replacing gradient descent with a budgeted propose-and-select search paradigm. It exploits a sample-wise decomposition of the transport objective to compute per-row impact scores and enforce a top-k intervention budget, focusing edits on the most influential samples. To guide candidate generation without predictor gradients, DISCOVER introduces an OT-guided cone sampling primitive driven by input-side transport geometry. Experiments on multiple tabular datasets demonstrate strong joint alignment of input and output distributions, extending distributional counterfactual reasoning to modern black box learning pipelines. A code repository is available at: https://github.com/VALHALLA9/Discover.