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

TL;DR

This paper introduces Flow IV, a method leveraging instrumental variables and normalizing flows to enable counterfactual inference in complex nonseparable outcome models.

Contribution

It extends IV-based counterfactual prediction to nonseparable models with invertible, triangular outcome functions, using normalizing flows for estimation.

Findings

Identifiability of treatment-outcome relationship under specified assumptions.

Proposed method effectively learns outcome functions for counterfactual inference.

Addresses limitations of existing IV methods for complex outcome models.

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 perform counterfactual inference. We refer to the method as Flow IV.