🤖 AI Summary
Existing attribution methods struggle to simultaneously achieve diversity, plausibility, and feasibility in counterfactual explanations. This work proposes a tractable attribution distribution framework that, for the first time, explicitly models an individual’s feasible attribution space using a closed-form probability distribution. By integrating probabilistic circuits with exponential tilting, the approach enables explicit control over the proximity and sparsity of generated counterfactuals through tilting parameters—without requiring model retraining. The attribution distribution is constructed using a cost-aware function that accounts for both feature proximity and modification costs. Evaluated on standard benchmarks, the method achieves high diversity, plausibility, and feasibility while maintaining efficient rejection sampling. Visualizations on MNIST further demonstrate that the tilting strength offers a controllable trade-off between proximity and validity of counterfactual suggestions.
📝 Abstract
Algorithmic recourse seeks to help individuals reverse unfavorable automated decisions by recommending actionable changes that achieve a desired outcome. As an individual usually has several distinct routes to a favorable decision, and different people can act on different ones, a recourse system should offer multiple realistic alternatives rather than one. Existing approaches formulate recourse as an optimization problem that constructs one or a small set of counterfactuals rather than modeling the underlying space of feasible solutions, and in practice each sacrifices diversity, plausibility, or feasibility to secure the others. We propose Tractable Recourse Distributions, a probabilistic framework that represents the space of feasible alternatives for a given factual instance as a probability distribution over favorable outcomes. For commonly used cost functions based on proximity and the number of feature changes, we show that this distribution admits an exact representation as a probabilistic circuit, obtained by exponentially tilting the circuit; each individual's distribution is therefore available in closed form, without retraining the model. Sampling from these distributions naturally produces diverse and plausible recourses, while the tilting parameters provide explicit control over their proximity and sparsity. Experiments on standard algorithmic recourse benchmark datasets demonstrate that the proposed framework attains diversity, plausibility, and feasibility simultaneously, while retaining sufficient probability mass over feasible counterfactuals for rejection sampling to be practical. A visual study on MNIST illustrates how the tilt strength trades proximity against validity.