Autoregressive flow-based causal discovery and inference

TL;DR

This paper introduces a unified autoregressive flow-based framework for causal discovery, inference, and counterfactual analysis, leveraging flow models' density estimation and invertibility to outperform existing methods on synthetic and benchmark datasets.

Contribution

It proposes a novel flow-based architecture that performs causal discovery, interventional, and counterfactual inference within a single model, exploiting the causal ordering inherent in autoregressive flows.

Findings

Outperforms alternative methods on synthetic data

Achieves competitive results on Cause-Effect Pairs benchmark

Enables direct evaluation of interventional and counterfactual predictions

Abstract

We posit that autoregressive flow models are well-suited to performing a range of causal inference tasks - ranging from causal discovery to making interventional and counterfactual predictions. In particular, we exploit the fact that autoregressive architectures define an ordering over variables, analogous to a causal ordering, in order to propose a single flow architecture to perform all three aforementioned tasks. We first leverage the fact that flow models estimate normalized log-densities of data to derive a bivariate measure of causal direction based on likelihood ratios. Whilst traditional measures of causal direction often require restrictive assumptions on the nature of causal relationships (e.g., linearity),the flexibility of flow models allows for arbitrary causal dependencies. Our approach compares favourably against alternative methods on synthetic data as well as on the Cause-Effect Pairs bench-mark dataset. Subsequently, we demonstrate that the invertible nature of flows naturally allows for direct evaluation of both interventional and counterfactual predictions, which require marginalization and conditioning over latent variables respectively. We present examples over synthetic data where autoregressive flows, when trained under the correct causal ordering, are able to make accurate interventional and counterfactual predictions