Counterfactuals answer questions of what would have been observed under altered circumstances and can therefore offer valuable insights. Whereas the classical interventional interpretation of counterfactuals has been studied extensively, backtracking constitutes a less studied alternative where all causal laws are kept intact. In the present work, we introduce a practical method called deep backtracking counterfactuals (DeepBC) for computing backtracking counterfactuals in structural causal models that consist of deep generative components. We propose two distinct versions of our method--one utilizing Langevin Monte Carlo sampling and the other employing constrained optimization--to generate counterfactuals for high-dimensional data. As a special case, our formulation reduces to methods in the field of counterfactual explanations. Compared to these, our approach represents a causally compliant, versatile and modular alternative. We demonstrate these properties experimentally on a modified version of MNIST and CelebA.

翻译：反事实问题探讨在改变条件下本应观察到的结果，因此能提供有价值的洞见。经典的反事实干预解释已被广泛研究，而回溯方法作为一种替代方案，保持了所有因果法则的完整性，但研究相对较少。本文提出一种名为“深度回溯反事实”（DeepBC）的实用方法，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。我们提出了两种不同的版本——一种利用朗之万蒙特卡洛采样，另一种采用约束优化——以生成高维数据的反事实样本。作为特例，我们的框架可转化为反事实解释领域的现有方法。与这些方法相比，我们的方法具有因果合规性、通用性和模块化优势。我们通过修改后的MNIST和CelebA数据集实验验证了这些特性。