# Deep Structural Causal Models for Tractable Counterfactual Inference

arXiv: https://arxiv.org/abs/2006.06485 · HTML: https://mlsanity.com/paper/2006.06485/

## Key facts

- Cited by 211 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

## Built on by (most cited first, 30 of 211)

- [HalluciDoctor: Mitigating Hallucinatory Toxicity in Visual Instruction Data](https://mlsanity.com/paper/2311.13614/) (2023)
- [Diffusion Visual Counterfactual Explanations](https://mlsanity.com/paper/2210.11841/) (2022)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Learning from Counterfactual Links for Link Prediction](https://mlsanity.com/paper/2106.02172/) (2021)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Beyond Trivial Counterfactual Explanations with Diverse Valuable Explanations](https://mlsanity.com/paper/2103.10226/) (2021)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [What is Healthy? Generative Counterfactual Diffusion for Lesion Localization](https://mlsanity.com/paper/2207.12268/) (2022)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [Learning Disentangled Representations in the Imaging Domain](https://mlsanity.com/paper/2108.12043/) (2021)
- [A Causal Lens for Controllable Text Generation](https://mlsanity.com/paper/2201.09119/) (2022)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Relating Graph Neural Networks to Structural Causal Models](https://mlsanity.com/paper/2109.04173/) (2021)
- [Measuring axiomatic soundness of counterfactual image models](https://mlsanity.com/paper/2303.01274/) (2023)
- [GaitGCI: Generative Counterfactual Intervention for Gait Recognition](https://mlsanity.com/paper/2306.03428/) (2023)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Sparse Visual Counterfactual Explanations in Image Space](https://mlsanity.com/paper/2205.07972/) (2022)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [Towards Trustworthy and Aligned Machine Learning: A Data-centric Survey with Causality Perspectives](https://mlsanity.com/paper/2307.16851/) (2023)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Counterfactual harm](https://mlsanity.com/paper/2204.12993/) (2022)
- [D'ARTAGNAN: Counterfactual Video Generation](https://mlsanity.com/paper/2206.01651/) (2022)
- [Generating Realistic Brain MRIs via a Conditional Diffusion Probabilistic Model](https://mlsanity.com/paper/2212.08034/) (2022)
- [RadEdit: stress-testing biomedical vision models via diffusion image editing](https://mlsanity.com/paper/2312.12865/) (2023)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [Self-Interpretable Time Series Prediction with Counterfactual Explanations](https://mlsanity.com/paper/2306.06024/) (2023)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)

## Abstract (arXiv)

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.