# Amortized Counterfactual Prediction with Graph Neural Networks

arXiv: https://arxiv.org/abs/2610.13724 · HTML: https://mlsanity.com/paper/2610.13724/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 67 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Meta-Learning Probabilistic Inference For Prediction](https://mlsanity.com/paper/1805.09921/) (2018)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [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)
- [Relating Graph Neural Networks to Structural Causal Models](https://mlsanity.com/paper/2109.04173/) (2021)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2110.14690/) (2021)
- [Graph Neural Processes for Spatio-Temporal Extrapolation](https://mlsanity.com/paper/2305.18719/) (2023)
- [Translation Equivariant Transformer Neural Processes](https://mlsanity.com/paper/2406.12409/) (2024)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Causal Feature Selection via Orthogonal Search](https://mlsanity.com/paper/2007.02938/) (2020)
- [Unsupervised Total Variation Loss for Semi-supervised Deep Learning of Semantic Segmentation](https://mlsanity.com/paper/1605.01368/) (2016)
- [Counterfactual Generative Modeling with Variational Causal Inference](https://mlsanity.com/paper/2410.12730/) (2024)

## Abstract (arXiv)

Counterfactual inference asks how an observed outcome might have differed under different circumstances, such as whether a patient would have recovered had they received a different treatment. Such questions arise whenever decisions depend on the outcomes of alternatives that were not observed. Answering counterfactual queries generally requires knowledge of the underlying causal structure, which is often unavailable in practice. A common approach is therefore to first estimate the causal graph from observational data and then perform counterfactual inference. However, errors in the estimated causal graph can propagate to downstream counterfactual predictions. To address this challenge, we introduce the Counterfactual Graph Neural Process (CFGNP), an end-to-end approach that answers counterfactual queries directly from observational data without first estimating a causal graph. CFGNP uses Graph Neural Networks (GNNs) to exploit the dual-graph structure by restricting cross-world message passing to corresponding factual--counterfactual variables. Across synthetic and image-based benchmarks, CFGNP achieves stronger predictive performance than existing approaches, including on the German Loan benchmark, where it reduces MSE from 4.51 × 10-2 to 0.19 × 10-2. Furthermore, on synthetic causal graphs, a model trained only on 10-node graphs maintains strong predictive performance on graphs with up to 30 nodes, without retraining.