Counterfactual explanations utilize feature perturbations to analyze the
outcome of an original decision and recommend an actionable recourse. We argue
that it is beneficial to provide several alternative explanations rather than a
single point solution and propose a probabilistic paradigm to estimate a
diverse set of counterfactuals. Specifically, we treat the perturbations as
random variables endowed with prior distribution functions. This allows
sampling multiple counterfactuals from the posterior density, with the added
benefit of incorporating inductive biases, preserving domain specific
constraints and quantifying uncertainty in estimates. More importantly, we
leverage Bayesian hierarchical modeling to share information across different
subgroups of a population, which can both improve robustness and measure
fairness. A gradient based sampler with superior convergence characteristics
efficiently computes the posterior samples. Experiments across several datasets
demonstrate that the counterfactuals estimated using our approach are valid,
sparse, diverse and feasible.

本文提出一个新的概率模型，用于计算模型的多个对抗性解释。该模型可以共享群体分组的信息，并保留领域特定的约束条件，同时评估不确定性，并得出合理、稀疏、多样和可行的结果。