# Neural Causal Models for Counterfactual Identification and Estimation

arXiv: https://arxiv.org/abs/2210.00035 · HTML: https://mlsanity.com/paper/2210.00035/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 78 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [A Framework For Contrastive Self-Supervised Learning And Designing A New Approach](https://mlsanity.com/paper/2009.00104/) (2020)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [Relating Graph Neural Networks to Structural Causal Models](https://mlsanity.com/paper/2109.04173/) (2021)
- [Nested Counterfactual Identification from Arbitrary Surrogate Experiments](https://mlsanity.com/paper/2107.03190/) (2021)
- [A Survey of Learning Causality with Data: Problems and Methods](https://mlsanity.com/paper/1809.09337/) (2018)
- [Adversarial Balancing-based Representation Learning for Causal Effect Inference with Observational Data](https://mlsanity.com/paper/1904.13335/) (2019)
- [Nonparametric causal effects based on incremental propensity score interventions](https://mlsanity.com/paper/1704.00211/) (2017)
- [Probabilistic Reasoning across the Causal Hierarchy](https://mlsanity.com/paper/2001.02889/) (2020)
- [VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2110.14690/) (2021)
- [Causal Identification under Markov Equivalence](https://mlsanity.com/paper/1812.06209/) (2018)
- [SBI: A Simulation-Based Test of Identifiability for Bayesian Causal Inference](https://mlsanity.com/paper/2102.11761/) (2021)

## Built on by (most cited first, 30 of 57)

- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Causal Interpretation of Self-Attention in Pre-Trained Transformers](https://mlsanity.com/paper/2310.20307/) (2023)
- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Counterfactual Image Editing](https://mlsanity.com/paper/2403.09683/) (2024)
- [Towards Causal Foundation Model: on Duality between Causal Inference and Attention](https://mlsanity.com/paper/2310.00809/) (2023)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Response](https://mlsanity.com/paper/2402.17233/) (2024)
- [Mitigating attribute amplification in counterfactual image generation](https://mlsanity.com/paper/2403.09422/) (2024)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [CF-Seg: Counterfactuals meet Segmentation](https://mlsanity.com/paper/2506.16213/) (2025)
- [Modular Learning of Deep Causal Generative Models for High-dimensional Causal Inference](https://mlsanity.com/paper/2401.01426/) (2024)
- [Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challenges](https://mlsanity.com/paper/2405.05025/) (2024)
- [The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning](https://mlsanity.com/paper/2410.09600/) (2024)
- [DeCaFlow: A deconfounding causal generative model](https://mlsanity.com/paper/2503.15114/) (2025)
- [Counterfactual Concept Bottleneck Models](https://mlsanity.com/paper/2402.01408/) (2024)
- [Latent Causal Modeling for 3D Brain MRI Counterfactuals](https://mlsanity.com/paper/2409.05585/) (2024)
- [Deep Autoregressive Models as Causal Inference Engines](https://mlsanity.com/paper/2409.18581/) (2024)
- [Counterfactual Identifiability via Dynamic Optimal Transport](https://mlsanity.com/paper/2510.08294/) (2025)
- [Causality from Bottom to Top: A Survey](https://mlsanity.com/paper/2403.11219/) (2024)
- [Consistency of Neural Causal Partial Identification](https://mlsanity.com/paper/2405.15673/) (2024)
- [Consistent End-to-End Estimation for Counterfactual Fairness](https://mlsanity.com/paper/2310.17687/) (2023)
- [Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimand](https://mlsanity.com/paper/2402.07419/) (2024)
- [CausalMan: A physics-based simulator for large-scale causality](https://mlsanity.com/paper/2502.12707/) (2025)
- [Interpretable Neural Causal Models with TRAM-DAGs](https://mlsanity.com/paper/2503.16206/) (2025)

## Abstract (arXiv)

Evaluating hypothetical statements about how the world would be had a different course of action been taken is arguably one key capability expected from modern AI systems. Counterfactual reasoning underpins discussions in fairness, the determination of blame and responsibility, credit assignment, and regret. In this paper, we study the evaluation of counterfactual statements through neural models. Specifically, we tackle two causal problems required to make such evaluations, i.e., counterfactual identification and estimation from an arbitrary combination of observational and experimental data. First, we show that neural causal models (NCMs) are expressive enough and encode the structural constraints necessary for performing counterfactual reasoning. Second, we develop an algorithm for simultaneously identifying and estimating counterfactual distributions. We show that this algorithm is sound and complete for deciding counterfactual identification in general settings. Third, considering the practical implications of these results, we introduce a new strategy for modeling NCMs using generative adversarial networks. Simulations corroborate with the proposed methodology.