# Perfect Match: A Simple Method for Learning Representations For Counterfactual Inference With Neural Networks

arXiv: https://arxiv.org/abs/1810.00656 · HTML: https://mlsanity.com/paper/1810.00656/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2018.

## Built on by (most cited first, 30 of 56)

- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [D'ARTAGNAN: Counterfactual Video Generation](https://mlsanity.com/paper/2206.01651/) (2022)
- [Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2202.01336/) (2022)
- [Evaluation Methods and Measures for Causal Learning Algorithms](https://mlsanity.com/paper/2202.02896/) (2022)
- [Causal Balancing for Domain Generalization](https://mlsanity.com/paper/2206.05263/) (2022)
- [Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation](https://mlsanity.com/paper/2311.11321/) (2023)
- [Estimating Categorical Counterfactuals via Deep Twin Networks](https://mlsanity.com/paper/2109.01904/) (2021)
- [VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2110.14690/) (2021)
- [GeneDisco: A Benchmark for Experimental Design in Drug Discovery](https://mlsanity.com/paper/2110.11875/) (2021)
- [Towards Causal Foundation Model: on Duality between Causal Inference and Attention](https://mlsanity.com/paper/2310.00809/) (2023)
- [DESCN: Deep Entire Space Cross Networks for Individual Treatment Effect Estimation](https://mlsanity.com/paper/2207.09920/) (2022)
- [NCoRE: Neural Counterfactual Representation Learning for Combinations of Treatments](https://mlsanity.com/paper/2103.11175/) (2021)
- [Causal Effect Estimation: Recent Advances, Challenges, and Opportunities](https://mlsanity.com/paper/2302.00848/) (2023)
- [Continual Causal Inference with Incremental Observational Data](https://mlsanity.com/paper/2303.01775/) (2023)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [A Survey of Deep Causal Models and Their Industrial Applications](https://mlsanity.com/paper/2209.08860/) (2022)
- [Learning Infomax and Domain-Independent Representations for Causal Effect Inference with Real-World Data](https://mlsanity.com/paper/2202.10885/) (2022)
- [Task-Driven Causal Feature Distillation: Towards Trustworthy Risk Prediction](https://mlsanity.com/paper/2312.16113/) (2023)
- [Estimating Potential Outcome Distributions with Collaborating Causal Networks](https://mlsanity.com/paper/2110.01664/) (2021)
- [Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothing](https://mlsanity.com/paper/2401.15447/) (2024)
- [Multi-Task Adversarial Learning for Treatment Effect Estimation in Basket Trials](https://mlsanity.com/paper/2203.05123/) (2022)
- [Deep Treatment-Adaptive Network for Causal Inference](https://mlsanity.com/paper/2112.13502/) (2021)
- [Covariate-Balancing-Aware Interpretable Deep Learning models for Treatment Effect Estimation](https://mlsanity.com/paper/2203.03185/) (2022)
- [Orthogonal Representation Learning for Estimating Causal Quantities](https://mlsanity.com/paper/2502.04274/) (2025)
- [Meta-Learners for Estimation of Causal Effects: Finite Sample Cross-Fit Performance](https://mlsanity.com/paper/2201.12692/) (2022)
- [Estimation of individual causal effects in network setup for multiple treatments](https://mlsanity.com/paper/2312.11573/) (2023)
- [Grab the Reins of Crowds: Estimating the Effects of Crowd Movement Guidance Using Causal Inference](https://mlsanity.com/paper/2102.03980/) (2021)
- [Is More Data All You Need? A Causal Exploration](https://mlsanity.com/paper/2206.02409/) (2022)
- [Pareto Invariant Representation Learning for Multimedia Recommendation](https://mlsanity.com/paper/2308.04706/) (2023)
- [PairNet: Training with Observed Pairs to Estimate Individual Treatment Effect](https://mlsanity.com/paper/2406.03864/) (2024)

## Abstract (arXiv)

Learning representations for counterfactual inference from observational data is of high practical relevance for many domains, such as healthcare, public policy and economics. Counterfactual inference enables one to answer "What if...?" questions, such as "What would be the outcome if we gave this patient treatment t1?". However, current methods for training neural networks for counterfactual inference on observational data are either overly complex, limited to settings with only two available treatments, or both. Here, we present Perfect Match (PM), a method for training neural networks for counterfactual inference that is easy to implement, compatible with any architecture, does not add computational complexity or hyperparameters, and extends to any number of treatments. PM is based on the idea of augmenting samples within a minibatch with their propensity-matched nearest neighbours. Our experiments demonstrate that PM outperforms a number of more complex state-of-the-art methods in inferring counterfactual outcomes across several benchmarks, particularly in settings with many treatments.