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测条件下，若情境发生改变本应观察到何种结果，从而提供宝贵见解。尽管反事实的经典干预性解释已被广泛研究，但回溯原则作为一种替代哲学——主张保持所有因果律不变——仍属较新探索。本文提出一种实用方法，用于计算包含深度生成组件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，使得在因果模型的结构化潜空间内求解可处理的约束优化问题即可生成反事实。我们的公式化方法还有助于与反事实解释领域的方法进行比较。相较于这些方法，我们的方法代表了一种灵活、模块化且因果兼容的替代方案。我们通过修改版MNIST和CelebA数据集上的实验验证了这些特性。