# Intact-VAE: Estimating Treatment Effects under Unobserved Confounding

arXiv: https://arxiv.org/abs/2101.06662 · HTML: https://mlsanity.com/paper/2101.06662/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 17 Jan 2021.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [CausalVAE: Structured Causal Disentanglement in Variational Autoencoder](https://mlsanity.com/paper/2004.08697/) (2020)
- [Using Embeddings to Correct for Unobserved Confounding in Networks](https://mlsanity.com/paper/1902.04114/) (2019)
- [Causal Inference with Noisy and Missing Covariates via Matrix Factorization](https://mlsanity.com/paper/1806.00811/) (2018)
- [Generalizing causal inferences from individuals in randomized trials to all trial-eligible individuals](https://mlsanity.com/paper/1709.04589/) (2017)
- [Causal Mosaic: Cause-Effect Inference via Nonlinear ICA and Ensemble Method](https://mlsanity.com/paper/2001.01894/) (2020)
- [A Universal Approximation Theorem of Deep Neural Networks for Expressing Probability Distributions](https://mlsanity.com/paper/2004.08867/) (2020)

## Built on by (most cited first, 10 of 10)

- [β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap](https://mlsanity.com/paper/2110.05225/) (2021)
- [Towards Principled Causal Effect Estimation by Deep Identifiable Models](https://mlsanity.com/paper/2109.15062/) (2021)
- [A Free Lunch with Influence Functions? Improving Neural Network Estimates with Concepts from Semiparametric Statistics](https://mlsanity.com/paper/2202.09096/) (2022)
- [Assisting Clinical Decisions for Scarcely Available Treatment via Disentangled Latent Representation](https://mlsanity.com/paper/2307.03315/) (2023)
- [High Dimensional Causal Inference with Variational Backdoor Adjustment](https://mlsanity.com/paper/2310.06100/) (2023)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [Trying to Outrun Causality with Machine Learning: Limitations of Model Explainability Techniques for Identifying Predictive Variables](https://mlsanity.com/paper/2202.09875/) (2022)
- [SLEM: Machine Learning for Path Modeling and Causal Inference with Super Learner Equation Modeling](https://mlsanity.com/paper/2308.04365/) (2023)
- [Active and Passive Causal Inference Learning](https://mlsanity.com/paper/2308.09248/) (2023)
- [Disentangled Graph Autoencoder for Treatment Effect Estimation](https://mlsanity.com/paper/2412.14497/) (2024)

## Abstract (arXiv)

NOTE: This preprint has a flawed theoretical formulation. Please avoid it and refer to the ICLR22 publication https://openreview.net/forum?id=q7n2RngwOM. Also, arXiv:2109.15062 contains some new ideas on unobserved Confounding. As an important problem of causal inference, we discuss the identification and estimation of treatment effects under unobserved confounding. Representing the confounder as a latent variable, we propose Intact-VAE, a new variant of variational autoencoder (VAE), motivated by the prognostic score that is sufficient for identifying treatment effects. We theoretically show that, under certain settings, treatment effects are identified by our model, and further, based on the identifiability of our model (i.e., determinacy of representation), our VAE is a consistent estimator with representation balanced for treatment groups. Experiments on (semi-)synthetic datasets show state-of-the-art performance under diverse settings.