# Towards Principled Causal Effect Estimation by Deep Identifiable Models

arXiv: https://arxiv.org/abs/2109.15062 · HTML: https://mlsanity.com/paper/2109.15062/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 93 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 30 of 33)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [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)
- [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)
- [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)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [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)
- [The Variational Method of Moments](https://mlsanity.com/paper/2012.09422/) (2020)
- [Causal Mosaic: Cause-Effect Inference via Nonlinear ICA and Ensemble Method](https://mlsanity.com/paper/2001.01894/) (2020)
- [Increasing the efficiency of randomized trial estimates via linear adjustment for a prognostic score](https://mlsanity.com/paper/2012.09935/) (2020)

## Built on by (most cited first, 4 of 4)

- [Deep Multi-Modal Structural Equations For Causal Effect Estimation With Unstructured Proxies](https://mlsanity.com/paper/2203.09672/) (2022)
- [β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap](https://mlsanity.com/paper/2110.05225/) (2021)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [Spatial Deconfounder: Interference-Aware Deconfounding for Spatial Causal Inference](https://mlsanity.com/paper/2510.08762/) (2025)

## Abstract (arXiv)

As an important problem in causal inference, we discuss the estimation of treatment effects (TEs). 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 TEs. Our VAE also naturally gives representations balanced for treatment groups, using its prior. Experiments on (semi-)synthetic datasets show state-of-the-art performance under diverse settings, including unobserved confounding. Based on the identifiability of our model, we prove identification of TEs under unconfoundedness, and also discuss (possible) extensions to harder settings.