# Leveraging a Simulator for Learning Causal Representations from Post-Treatment Covariates for CATE

arXiv: https://arxiv.org/abs/2502.05037 · HTML: https://mlsanity.com/paper/2502.05037/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 69 references that are in the map.
- First posted on arXiv 7 Feb 2025.

## Builds on (most cited first, 30 of 32)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Diffusion Models for Counterfactual Explanations](https://mlsanity.com/paper/2203.15636/) (2022)
- [Generate Your Counterfactuals: Towards Controlled Counterfactual Generation for Text](https://mlsanity.com/paper/2012.04698/) (2020)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Perfect Match: A Simple Method for Learning Representations For Counterfactual Inference With Neural Networks](https://mlsanity.com/paper/1810.00656/) (2018)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [DoCoGen: Domain Counterfactual Generation for Low Resource Domain Adaptation](https://mlsanity.com/paper/2202.12350/) (2022)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [DISCO: Distilling Counterfactuals with Large Language Models](https://mlsanity.com/paper/2212.10534/) (2022)
- [In Search of Insights, Not Magic Bullets: Towards Demystification of the Model Selection Dilemma in Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2302.02923/) (2023)
- [BiomedJourney: Counterfactual Biomedical Image Generation by Instruction-Learning from Multimodal Patient Journeys](https://mlsanity.com/paper/2310.10765/) (2023)
- [A Survey on Simulators for Testing Self-Driving Cars](https://mlsanity.com/paper/2101.05337/) (2021)
- [Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2202.01336/) (2022)
- [CORE: A Retrieve-then-Edit Framework for Counterfactual Data Generation](https://mlsanity.com/paper/2210.04873/) (2022)
- [Counterfactual Image Editing](https://mlsanity.com/paper/2403.09683/) (2024)
- [Designing Counterfactual Generators using Deep Model Inversion](https://mlsanity.com/paper/2109.14274/) (2021)
- [Adversarial Balancing for Causal Inference](https://mlsanity.com/paper/1810.07406/) (2018)
- [Minimax Optimal Nonparametric Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/2002.06471/) (2020)
- [Adversarial De-confounding in Individualised Treatment Effects Estimation](https://mlsanity.com/paper/2210.10530/) (2022)

## Abstract (arXiv)

Treatment effect estimation involves assessing the impact of different treatments on individual outcomes. Current methods estimate Conditional Average Treatment Effect (CATE) using observational datasets where covariates are collected before treatment assignment and outcomes are observed afterward, under assumptions like positivity and unconfoundedness. In this paper, we address a scenario where both covariates and outcomes are gathered after treatment. We show that post-treatment covariates render CATE unidentifiable, and recovering CATE requires learning treatment-independent causal representations. Prior work shows that such representations can be learned through contrastive learning if counterfactual supervision is available in observational data. However, since counterfactuals are rare, other works have explored using simulators that offer synthetic counterfactual supervision. Our goal in this paper is to systematically analyze the role of simulators in estimating CATE. We analyze the CATE error of several baselines and highlight their limitations. We then establish a generalization bound that characterizes the CATE error from jointly training on real and simulated distributions, as a function of the real-simulator mismatch. Finally, we introduce SimPONet, a novel method whose loss function is inspired from our generalization bound. We further show how SimPONet adjusts the simulator's influence on the learning objective based on the simulator's relevance to the CATE task. We experiment with various DGPs, by systematically varying the real-simulator distribution gap to evaluate SimPONet's efficacy against state-of-the-art CATE baselines.