mlsanityData to 7 Oct 2026

Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model

arXiv 2306.01424 ↗First posted 2 Jun 2023stat.ML cs.LGcited by 14

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Abstract (arXiv)

Counterfactual inference aims to answer retrospective "what if" questions and thus belongs to the most fine-grained type of inference in Pearl's causality ladder. Existing methods for counterfactual inference with continuous outcomes aim at point identification and thus make strong and unnatural assumptions about the underlying structural causal model. In this paper, we relax these assumptions and aim at partial counterfactual identification of continuous outcomes, i.e., when the counterfactual query resides in an ignorance interval with informative bounds. We prove that, in general, the ignorance interval of the counterfactual queries has non-informative bounds, already when functions of structural causal models are continuously differentiable. As a remedy, we propose a novel sensitivity model called Curvature Sensitivity Model. This allows us to obtain informative bounds by bounding the curvature of level sets of the functions. We further show that existing point counterfactual identification methods are special cases of our Curvature Sensitivity Model when the bound of the curvature is set to zero. We then propose an implementation of our Curvature Sensitivity Model in the form of a novel deep generative model, which we call Augmented Pseudo-Invertible Decoder. Our implementation employs (i) residual normalizing flows with (ii) variational augmentations. We empirically demonstrate the effectiveness of our Augmented Pseudo-Invertible Decoder. To the best of our knowledge, ours is the first partial identification model for Markovian structural causal models with continuous outcomes.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 91 of its 153 references that are in the map. First posted on arXiv 2 Jun 2023.

Builds on

91 of 153 references.

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Citing papers per year: 2023: 3; 2024: 4; 2025: 5; 2026: 2.

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  1. 2023A Neural Framework for Generalized Causal Sensitivity Analysiscited by 17
  2. 2023Causal Fairness under Unobserved Confounding: A Neural Sensitivity Frameworkcited by 10
  3. 2024Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learnercited by 10
  4. 2024Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challengescited by 8
  5. 2025Counterfactual Identifiability via Dynamic Optimal Transportcited by 5
  6. 2023Consistent End-to-End Estimation for Counterfactual Fairnesscited by 4
  7. 2024Targeted Sequential Indirect Experiment Designcited by 4
  8. 2024Consistency of Neural Causal Partial Identificationcited by 3
  9. 2025Your Assumed DAG is Wrong and Here's How To Deal With Itcited by 1
  10. 2026Causal Inference on Networks under Misspecified Exposure Mappings: A Partial Identification Frameworkcited by 1
  11. 2025Learning Counterfactual Outcomes Under Rank Preservationcited by 0
  12. 2025Learning Counterfactually Fair Models via Improved Generation with Neural Causal Modelscited by 0
2 more
  1. 2025Testing for Causal Fairnesscited by 0
  2. 2026ConfoundingSHAP: Quantifying confounding strength in causal inferencecited by 0