Counterfactuals can offer valuable insights by answering what would have been observed under altered circumstances, conditional on a factual observation. Whereas the classical interventional interpretation of counterfactuals has been studied extensively, backtracking constitutes a less studied alternative the backtracking principle has emerged as an alternative philosophy where all causal laws are kept intact. In the present work, we introduce a practical method for computing backtracking counterfactuals in structural causal models that consist of deep generative components. To this end, we impose conditions on the structural assignments that enable the generation of counterfactuals by solving a tractable constrained optimization problem in the structured latent space of a causal model. Our formulation also facilitates a comparison with methods in the field of counterfactual explanations. Compared to these, our method represents a versatile, modular and causally compliant alternative. We demonstrate these properties experimentally on a modified version of MNIST and CelebA.

翻译：反事实通过回答在事实观察条件下、改变情境本应产生何种结果，可提供宝贵见解。尽管反事实的经典干预性解释已被广泛研究，但回溯性原则作为另一种哲学理念——保持所有因果律不变——仍是较少被探索的替代方案。本文提出一种实用方法，用于计算由深度生成组件构成的结构因果模型中的回溯反事实。为此，我们对结构赋值施加约束条件，使其能够通过求解结构化隐空间中可处理的约束优化问题生成反事实。本方法还便于与反事实解释领域的方法进行比较。相较而言，我们的方法是一种通用、模块化且符合因果原则的替代方案。我们通过修改版MNIST和CelebA数据集实验验证了这些特性。