# Causal Effect Estimation using identifiable Variational AutoEncoder with Latent Confounders and Post-Treatment Variables

arXiv: https://arxiv.org/abs/2408.07219 · HTML: https://mlsanity.com/paper/2408.07219/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 13 Aug 2024.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [A causal framework for discovering and removing direct and indirect discrimination](https://mlsanity.com/paper/1611.07509/) (2016)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Simple and Effective VAE Training with Calibrated Decoders](https://mlsanity.com/paper/2006.13202/) (2020)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [A Survey of Learning Causality with Data: Problems and Methods](https://mlsanity.com/paper/1809.09337/) (2018)
- [Information Constraints on Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1805.08672/) (2018)
- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Ivy: Instrumental Variable Synthesis for Causal Inference](https://mlsanity.com/paper/2004.05316/) (2020)
- [Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder](https://mlsanity.com/paper/2310.01937/) (2023)
- [Long-term Causal Effects Estimation via Latent Surrogates Representation Learning](https://mlsanity.com/paper/2208.04589/) (2022)
- [Disentangled Representation for Causal Mediation Analysis](https://mlsanity.com/paper/2302.09694/) (2023)
- [Causal Decision Trees](https://mlsanity.com/paper/1508.03812/) (2015)

## Built on by (most cited first, 1 of 1)

- [Coupling Generative Modeling and an Autoencoder with the Causal Bridge](https://mlsanity.com/paper/2509.25599/) (2025)

## Abstract (arXiv)

Estimating causal effects from observational data is challenging, especially in the presence of latent confounders. Much work has been done on addressing this challenge, but most of the existing research ignores the bias introduced by the post-treatment variables. In this paper, we propose a novel method of joint Variational AutoEncoder (VAE) and identifiable Variational AutoEncoder (iVAE) for learning the representations of latent confounders and latent post-treatment variables from their proxy variables, termed CPTiVAE, to achieve unbiased causal effect estimation from observational data. We further prove the identifiability in terms of the representation of latent post-treatment variables. Extensive experiments on synthetic and semi-synthetic datasets demonstrate that the CPTiVAE outperforms the state-of-the-art methods in the presence of latent confounders and post-treatment variables. We further apply CPTiVAE to a real-world dataset to show its potential application.