DISCOVER: A Solver for Distributional Counterfactual Explanations

TL;DR

DISCOVER is a model-agnostic solver for distributional counterfactual explanations that replaces gradient-based optimization with a propose-and-select search, enabling explanation generation for non-differentiable models in tabular data.

Contribution

It introduces a gradient-free, sample-wise decomposition approach for distributional counterfactuals, extending applicability to black-box models and complex data pipelines.

Findings

Effective in aligning input and output distributions across datasets

Enables counterfactual explanations for non-differentiable models

Maintains statistical certification with a new search paradigm

Abstract

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 sparse 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/understanding-ml/DCE.