Deep Backtracking Counterfactuals for Causally Compliant Explanations

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.