Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide explanations that help the affected individuals not only to understand why a prediction was output, but also how to act to obtain a desired outcome. To this end, several works have proposed optimization-based methods to generate nearest counterfactual explanations. However, these methods are often restricted to a particular subset of models (e.g., decision trees or linear models) and differentiable distance functions. In contrast, we build on standard theory and tools from formal verification and propose a novel algorithm that solves a sequence of satisfiability problems, where both the distance function (objective) and predictive model (constraints) are represented as logic formulae. As shown by our experiments on real-world data, our algorithm is: i) model-agnostic ({non-}linear, {non-}differentiable, {non-}convex); ii) data-type-agnostic (heterogeneous features); iii) distance-agnostic ($\ell_0, \ell_1, \ell_\infty$, and combinations thereof); iv) able to generate plausible and diverse counterfactuals for any sample (i.e., 100% coverage); and v) at provably optimal distances.

中文翻译：

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对结果决策的模型不可知反事实解释

在审前保释和贷款批准等背景下，预测模型越来越多地用于支持个人层面的相应决策。因此，越来越多的社会和法律压力要求提供解释，以帮助受影响的个人不仅了解为什么会输出预测，而且还了解如何采取行动以获得预期的结果。为此，一些工作提出了基于优化的方法来生成最接近的反事实解释。然而，这些方法通常限于特定的模型子集（例如，决策树或线性模型）和可微分距离函数。相比之下，我们建立在标准理论和形式验证工具的基础上，并提出了一种解决一系列可满足性问题的新算法，其中距离函数（目标）和预测模型（约束）都表示为逻辑公式。如图所示由我们的真实世界数据的实验中，我们的算法是：ⅰ）模型无关（{非}直链，{}非可微的，{}非凸）; ii) 数据类型不可知（异构特征）；iii) 距离不可知（$\ell_0、\ell_1、\ell_\infty$ 及其组合）；iv) 能够为任何样本生成合理且多样的反事实（即 100% 覆盖率）；v) 在可证明的最佳距离处。iv) 能够为任何样本生成合理且多样的反事实（即 100% 覆盖率）；v) 在可证明的最佳距离处。iv) 能够为任何样本生成合理且多样的反事实（即 100% 覆盖率）；v) 在可证明的最佳距离处。