[2508.01321] Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables

Statistics > Machine Learning arXiv:2508.01321 (stat) [Submitted on 2 Aug 2025 (v1), last revised 28 Mar 2026 (this version, v2)] Title:Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables Authors:Marc Braun, Jose M. Peña, Adel Daoud View a PDF of the paper titled Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables, by Marc Braun and Jose M. Pe\~na and Adel Daoud View PDF 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, then 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 ...