[Paper Review] Deep Structural Causal Models for Tractable Counterfactual Inference

Nick Pawlowski, Daniel C. Castro+1 more|arXiv (Cornell University)|Jun 11, 2020

Domain Adaptation and Few-Shot Learning65 references83 citations

TL;DR

This paper presents a unified framework for deep structural causal models (DSCMs) that enables tractable counterfactual inference by inferring exogenous noise with normalising flows and variational inference, demonstrated on Morpho-MNIST and brain MRI data.

ABSTRACT

We formulate a general framework for building structural causal models (SCMs) with deep learning components. The proposed approach employs normalising flows and variational inference to enable tractable inference of exogenous noise variables - a crucial step for counterfactual inference that is missing from existing deep causal learning methods. Our framework is validated on a synthetic dataset built on MNIST as well as on a real-world medical dataset of brain MRI scans. Our experimental results indicate that we can successfully train deep SCMs that are capable of all three levels of Pearl's ladder of causation: association, intervention, and counterfactuals, giving rise to a powerful new approach for answering causal questions in imaging applications and beyond. The code for all our experiments is available at https://github.com/biomedia-mira/deepscm.

Motivation & Objective

• Provide a unified framework for structural causal models (SCMs) with deep learning components.
• Enable tractable counterfactual inference by arguing for inferring exogenous noise via variational inference or normalising flows.
• Demonstrate the approach on synthetic Morpho-MNIST data to validate causal reasoning across Pearl's ladder of causation (association, intervention, counterfactuals).
• Demonstrate real-world applicability on brain MRI data to illustrate counterfactual reasoning in medical imaging.

Proposed method

• Introduce three classes of deep causal mechanisms: invertible explicit-likelihood, amortised explicit-likelihood, and amortised implicit-likelihood mechanisms.
• Use normalising flows to model invertible components and variational/inference techniques to handle abduction.
• Formulate counterfactual inference as a three-step process (abduction, action, prediction) with tractable inference for exogenous noises.
• Allow conditioning on parents via conditional flows and modular deep components to build scalable, structured DSCMs.
• Provide Monte Carlo sampling procedures to generate counterfactual samples when exact computation is intractable.

Experimental results

Research questions

• RQ1 Can we build deep structural causal models that support association, intervention, and counterfactual reasoning for high-dimensional data?
• RQ2 How can exogenous noise be inferred tractably in DSCMs to enable unit-level counterfactuals?
• RQ3 Do DSCMs trained with normalising flows and variational inference produce plausible counterfactuals in imaging tasks?
• RQ4 What is the impact of different deep mechanism architectures on associative, interventional, and counterfactual capabilities?
• RQ5 Can the framework be validated on synthetic and real medical imaging data (e.g., Morpho-MNIST and brain MRI) to illustrate practical causal reasoning?

Key findings

• DSCMs can represent causal relationships in high-dimensional data and support all three levels of Pearl’s ladder of causation.
• Inferring exogenous noise via variational inference or normalising flows enables tractable abduction for counterfactuals.
• In Morpho-MNIST, the full causal model outperforms independent and conditional variants in capturing interdependencies and generating accurate counterfactuals (lower MAE for counterfactuals).
• In brain imaging, the DSCM demonstrates plausible counterfactuals showing how age, sex, brain, and ventricle volumes may interact under interventions.
• The three-model comparison on Morpho-MNIST provides quantitative evidence that incorporating causal structure improves likelihoods and reconstruction while enabling counterfactual generation.
• Counterfactual sampling can be performed via Monte Carlo to approximate distributions when exact inversion is intractable.