Causally Consistent Normalizing Flow

TL;DR

This paper introduces CCNF, a novel causally consistent normalizing flow model that maintains causal structure while approximating complex distributions, enabling effective causal inference and addressing fairness issues.

Contribution

CCNF is the first causally consistent normalizing flow that can approximate any distribution with multiple layers, using novel constructs to preserve causal structure without sacrificing expressiveness.

Findings

CCNF outperforms existing methods in causal inference tasks.

CCNF effectively addresses fairness issues in real-world datasets.

CCNF can handle interventions and counterfactuals seamlessly.

Abstract

Causal inconsistency arises when the underlying causal graphs captured by generative models like \textit{Normalizing Flows} (NFs) are inconsistent with those specified in causal models like \textit{Struct Causal Models} (SCMs). This inconsistency can cause unwanted issues including the unfairness problem. Prior works to achieve causal consistency inevitably compromise the expressiveness of their models by disallowing hidden layers. In this work, we introduce a new approach: \textbf{C}ausally \textbf{C}onsistent \textbf{N}ormalizing \textbf{F}low (CCNF). To the best of our knowledge, CCNF is the first causally consistent generative model that can approximate any distribution with multiple layers. CCNF relies on two novel constructs: a sequential representation of SCMs and partial causal transformations. These constructs allow CCNF to inherently maintain causal consistency without sacrificing expressiveness. CCNF can handle all forms of causal inference tasks, including interventions and counterfactuals. Through experiments, we show that CCNF outperforms current approaches in causal inference. We also empirically validate the practical utility of CCNF by applying it to real-world datasets and show how CCNF addresses challenges like unfairness effectively.