# VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries

arXiv: https://arxiv.org/abs/2110.14690 · HTML: https://mlsanity.com/paper/2110.14690/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 30 of 37)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Tighter Variational Bounds are Not Necessarily Better](https://mlsanity.com/paper/1802.04537/) (2018)
- [Graph Convolutional Encoders for Syntax-aware Neural Machine Translation](https://mlsanity.com/paper/1704.04675/) (2017)
- [Perfect Match: A Simple Method for Learning Representations For Counterfactual Inference With Neural Networks](https://mlsanity.com/paper/1810.00656/) (2018)
- [A Causal View on Robustness of Neural Networks](https://mlsanity.com/paper/2005.01095/) (2020)
- [Counterfactual Fairness with Disentangled Causal Effect Variational Autoencoder](https://mlsanity.com/paper/2011.11878/) (2020)
- [Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives](https://mlsanity.com/paper/1810.04152/) (2018)

## Built on by (most cited first, 19 of 19)

- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [DiffPO: A causal diffusion model for learning distributions of potential outcomes](https://mlsanity.com/paper/2410.08924/) (2024)
- [Don't Throw it Away! The Utility of Unlabeled Data in Fair Decision Making](https://mlsanity.com/paper/2205.04790/) (2022)
- [Emerging Synergies in Causality and Deep Generative Models: A Survey](https://mlsanity.com/paper/2301.12351/) (2023)
- [Deep Backtracking Counterfactuals for Causally Compliant Explanations](https://mlsanity.com/paper/2310.07665/) (2023)
- [DoubleGen: Debiased Generative Modeling of Counterfactuals](https://mlsanity.com/paper/2509.16842/) (2025)
- [On Root Cause Localization and Anomaly Mitigation through Causal Inference](https://mlsanity.com/paper/2212.04031/) (2022)
- [CausalMan: A physics-based simulator for large-scale causality](https://mlsanity.com/paper/2502.12707/) (2025)
- [Counterfactual Probabilistic Diffusion with Expert Models](https://mlsanity.com/paper/2508.13355/) (2025)
- [Diffusion Model in Causal Inference with Unmeasured Confounders](https://mlsanity.com/paper/2308.03669/) (2023)
- [CEPAE: Conditional Entropy-Penalized Autoencoders for Time Series Counterfactuals](https://mlsanity.com/paper/2602.15546/) (2026)
- [Debiased Counterfactual Generation via Flow Matching from Observations](https://mlsanity.com/paper/2605.07665/) (2026)
- [Teleporter Theory: A General and Simple Approach for Modeling Cross-World Counterfactual Causality](https://mlsanity.com/paper/2406.11501/) (2024)
- [Causal Representation Learning from Network Data](https://mlsanity.com/paper/2509.01916/) (2025)
- [Neurocircuitry-Inspired Hierarchical Graph Causal Attention Networks for Explainable Depression Identification](https://mlsanity.com/paper/2511.17622/) (2025)
- [JANUS: Structured Bidirectional Generation for Guaranteed Constraints and Analytical Uncertainty](https://mlsanity.com/paper/2603.03748/) (2026)
- [Amortized Counterfactual Prediction with Graph Neural Networks](https://mlsanity.com/paper/2610.13724/) (2026)

## Abstract (arXiv)

In this paper, we introduce VACA, a novel class of variational graph autoencoders for causal inference in the absence of hidden confounders, when only observational data and the causal graph are available. Without making any parametric assumptions, VACA mimics the necessary properties of a Structural Causal Model (SCM) to provide a flexible and practical framework for approximating interventions (do-operator) and abduction-action-prediction steps. As a result, and as shown by our empirical results, VACA accurately approximates the interventional and counterfactual distributions on diverse SCMs. Finally, we apply VACA to evaluate counterfactual fairness in fair classification problems, as well as to learn fair classifiers without compromising performance.