Counterfactual inference is the task of answering hypothetical "what-if" queries about a unit, given an observational dataset, modeling assumptions, and a causal graph. This enables a modeler to reason about hypothetical scenarios that cannot otherwise be answered without assumptions or a causal graph. The simpler case involves a causal graph with scalar 1-D variables that denote different attributes in the data-generation process. While the literature is clear in the 1-D case, extending this to settings with high-dimensional nodes (e.g., images) remains challenging. Conventionally, in the literature, methods recover the latent state from the factual image (inversion), generate counterfactual attributes from the graph, and render the counterfactual image from the latent state using the updated attributes. In our work, we investigate the necessity of the inversion step in computing high-dimensional counterfactuals. We first discuss moving from the scalar 1-D case to the higher-dimensional case. Secondly, we discuss the relevance of the inversion step and evaluate an inversion-free counterpart repurposed from the image-editing literature. Finally, on image datasets such as CelebA and ADNI, we benchmark our approach using two measures: namely, effectiveness and identity preservation. While effectiveness is a measure of how faithfully the counterfactual attribute is rendered, identity preservation measures whether the same unit (image) is being rendered, both of which are crucial for high-dimensional counterfactual inference. We present the tradeoffs of using inversion-based and inversion-free approaches in our work.

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