Deep Backtracking Counterfactuals for Causally Compliant Explanations

Counterfactuals answer questions of what would have been observed under altered circum-stances and can therefore offer valuable insights. Whereas the classical interventional in-terpretation 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 compo-nents. 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 com-pliant, versatile and modular alternative. We demonstrate these properties experimentally on a modified version of MNIST and CelebA.