# β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap

arXiv: https://arxiv.org/abs/2110.05225 · HTML: https://mlsanity.com/paper/2110.05225/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 85 references that are in the map.
- First posted on arXiv 11 Oct 2021.

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

- [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)
- [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)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [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)
- [Support and Invertibility in Domain-Invariant Representations](https://mlsanity.com/paper/1903.03448/) (2019)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [Using Embeddings to Correct for Unobserved Confounding in Networks](https://mlsanity.com/paper/1902.04114/) (2019)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [Causal Mosaic: Cause-Effect Inference via Nonlinear ICA and Ensemble Method](https://mlsanity.com/paper/2001.01894/) (2020)
- [Characterization of Overlap in Observational Studies](https://mlsanity.com/paper/1907.04138/) (2019)
- [Increasing the efficiency of randomized trial estimates via linear adjustment for a prognostic score](https://mlsanity.com/paper/2012.09935/) (2020)
- [Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness](https://mlsanity.com/paper/1712.04594/) (2017)
- [Intact-VAE: Estimating Treatment Effects under Unobserved Confounding](https://mlsanity.com/paper/2101.06662/) (2021)
- [Latent Causal Invariant Model](https://mlsanity.com/paper/2011.02203/) (2020)
- [Deconfounding Scores: Feature Representations for Causal Effect Estimation with Weak Overlap](https://mlsanity.com/paper/2104.05762/) (2021)
- [Towards Principled Causal Effect Estimation by Deep Identifiable Models](https://mlsanity.com/paper/2109.15062/) (2021)
- [Posterior Average Effects](https://mlsanity.com/paper/1906.06360/) (2019)

## Built on by (most cited first, 8 of 8)

- [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)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Graph-based Unsupervised Disentangled Representation Learning via Multimodal Large Language Models](https://mlsanity.com/paper/2407.18999/) (2024)
- [Causal Inference with Latent Variables: Recent Advances and Future Prospectives](https://mlsanity.com/paper/2406.13966/) (2024)
- [Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning](https://mlsanity.com/paper/2505.05192/) (2025)
- [ACTIVA: Amortized Causal Effect Estimation via Transformer-based Variational Autoencoder](https://mlsanity.com/paper/2503.01290/) (2025)
- [Cross-Domain Off-Policy Evaluation and Learning for Contextual Bandits](https://mlsanity.com/paper/2607.22012/) (2026)
- [Uncertainty-Guided LLM Semantic Augmentation for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2607.26599/) (2026)

## Abstract (arXiv)

As an important problem in causal inference, we discuss the identification and estimation of treatment effects (TEs) under limited overlap; that is, when subjects with certain features belong to a single treatment group. We use a latent variable to model a prognostic score which is widely used in biostatistics and sufficient for TEs; i.e., we build a generative prognostic model. We prove that the latent variable recovers a prognostic score, and the model identifies individualized treatment effects. The model is then learned as β-Intact-VAE--a new type of variational autoencoder (VAE). We derive the TE error bounds that enable representations balanced for treatment groups conditioned on individualized features. The proposed method is compared with recent methods using (semi-)synthetic datasets.