Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables

Marc Braun, Jose Peña, Adel Daoud
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:861-886, 2026.

Abstract

To reach human level intelligence, learning algorithms need to incorporate causal reasoning. But identifying causality, and particularly counterfactual reasoning, remains elusive. In this paper, we make progress on counterfactual inference in nonseparable outcome models by utilizing instrumental variables (IVs). IVs are a classic tool for mitigating bias from unobserved confounders when estimating causal effects. While IV methods for effect estimation have been extended to nonseparable outcome models under different assumptions, existing IV approaches to counterfactual prediction typically assume one-dimensional outcomes and additive noise. In this paper, we show that under standard IV assumptions, along with the assumption that the outcome function is invertible and has a triangular structure, the treatment–outcome relationship becomes identifiable from observed data. We furthermore propose a method to learn the outcome function utilizing normalizing flows. This outcome function estimator can then be used to perform counterfactual inference. We refer to the method as \textit{Flow IV}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-braun26a, title = {Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables}, author = {Braun, Marc and Pe{\~n}a, Jose and Daoud, Adel}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {861--886}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/braun26a/braun26a.pdf}, url = {https://proceedings.mlr.press/v323/braun26a.html}, abstract = {To reach human level intelligence, learning algorithms need to incorporate causal reasoning. But identifying causality, and particularly counterfactual reasoning, remains elusive. In this paper, we make progress on counterfactual inference in nonseparable outcome models by utilizing instrumental variables (IVs). IVs are a classic tool for mitigating bias from unobserved confounders when estimating causal effects. While IV methods for effect estimation have been extended to nonseparable outcome models under different assumptions, existing IV approaches to counterfactual prediction typically assume one-dimensional outcomes and additive noise. In this paper, we show that under standard IV assumptions, along with the assumption that the outcome function is invertible and has a triangular structure, the treatment–outcome relationship becomes identifiable from observed data. We furthermore propose a method to learn the outcome function utilizing normalizing flows. This outcome function estimator can then be used to perform counterfactual inference. We refer to the method as \textit{Flow IV}.} }
Endnote
%0 Conference Paper %T Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables %A Marc Braun %A Jose Peña %A Adel Daoud %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-braun26a %I PMLR %P 861--886 %U https://proceedings.mlr.press/v323/braun26a.html %V 323 %X To reach human level intelligence, learning algorithms need to incorporate causal reasoning. But identifying causality, and particularly counterfactual reasoning, remains elusive. In this paper, we make progress on counterfactual inference in nonseparable outcome models by utilizing instrumental variables (IVs). IVs are a classic tool for mitigating bias from unobserved confounders when estimating causal effects. While IV methods for effect estimation have been extended to nonseparable outcome models under different assumptions, existing IV approaches to counterfactual prediction typically assume one-dimensional outcomes and additive noise. In this paper, we show that under standard IV assumptions, along with the assumption that the outcome function is invertible and has a triangular structure, the treatment–outcome relationship becomes identifiable from observed data. We furthermore propose a method to learn the outcome function utilizing normalizing flows. This outcome function estimator can then be used to perform counterfactual inference. We refer to the method as \textit{Flow IV}.
APA
Braun, M., Peña, J. & Daoud, A.. (2026). Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:861-886 Available from https://proceedings.mlr.press/v323/braun26a.html.

Related Material