A Generalized-Bayes Perspective on Counterfactual Explanations: Posterior-Based Decision-Making and Evaluation

Counterfactual explanation (CE) is widely used to enhance the interpretability of machine learning models and support data-driven decision-making based on model predictions. However, existing CE methods typically require two exogenously specified inputs: a desired output value (target) and a distance function that quantifies changes in explanatory variables. In regression settings, neither the validity of target specification nor the practical interpretation of the distance metric has been sufficiently addressed. Furthermore, most existing CE methods focus on altering predictions rather than optimizing a decision objective, even though real-world decision-making often requires explicit objective maximization. To address these limitations, we formulate CE as a profit maximization problem in management and marketing contexts and propose a framework termed profit-based counterfactual explanation (PBCE). PBCE eliminates the need for exogenous target specification by directly maximizing profit as the primary optimization objective. Concurrently, the distance term is reinterpreted as the cost of modifying product attributes, providing a clear and economically grounded interpretation.

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.

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.