Gradient-based Counterfactual Explanations using Tractable Probabilistic Models
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Counterfactual examples are an appealing class of post-hoc explanations for machine learning models. Given input x of class y_1, its counterfactual is a contrastive example x^' of another class y_0. Current approaches primarily solve this task by a complex optimization: define an objective function based on the loss of the counterfactual outcome y_0 with hard or soft constraints, then optimize this function as a black-box. This "deep learning" approach, however, is rather slow, sometimes tricky, and may result in unrealistic counterfactual examples. In this work, we propose a novel approach to deal with these problems using only two gradient computations based on tractable probabilistic models. First, we compute an unconstrained counterfactual u of x to induce the counterfactual outcome y_0. Then, we adapt u to higher density regions, resulting in x^'. Empirical evidence demonstrates the dominant advantages of our approach.
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