# Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder

arXiv: https://arxiv.org/abs/2310.01937 · HTML: https://mlsanity.com/paper/2310.01937/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 54 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (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)
- [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)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [A causal framework for discovering and removing direct and indirect discrimination](https://mlsanity.com/paper/1611.07509/) (2016)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Valid Causal Inference with (Some) Invalid Instruments](https://mlsanity.com/paper/2006.11386/) (2020)
- [Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition](https://mlsanity.com/paper/2107.05884/) (2021)
- [Ivy: Instrumental Variable Synthesis for Causal Inference](https://mlsanity.com/paper/2004.05316/) (2020)
- [Causal Mediation Analysis with Hidden Confounders](https://mlsanity.com/paper/2102.11724/) (2021)
- [Finding and Listing Front-door Adjustment Sets](https://mlsanity.com/paper/2210.05816/) (2022)

## Built on by (most cited first, 17 of 17)

- [Causal Evaluation of Language Models](https://mlsanity.com/paper/2405.00622/) (2024)
- [Fairness Evaluation with Item Response Theory](https://mlsanity.com/paper/2411.02414/) (2024)
- [Causal Inference with Latent Variables: Recent Advances and Future Prospectives](https://mlsanity.com/paper/2406.13966/) (2024)
- [Causal Prompting for Implicit Sentiment Analysis with Large Language Models](https://mlsanity.com/paper/2507.00389/) (2025)
- [Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning](https://mlsanity.com/paper/2505.05192/) (2025)
- [Debiased Front-Door Learners for Heterogeneous Effects](https://mlsanity.com/paper/2509.22531/) (2025)
- [When to Trust: A Causality-Aware Calibration Framework for Accurate Knowledge Graph Retrieval-Augmented Generation](https://mlsanity.com/paper/2601.09241/) (2026)
- [Causal Effect Estimation using identifiable Variational AutoEncoder with Latent Confounders and Post-Treatment Variables](https://mlsanity.com/paper/2408.07219/) (2024)
- [FairDRL-ST: Disentangled Representation Learning for Fair Spatio-Temporal Mobility Prediction](https://mlsanity.com/paper/2508.07518/) (2025)
- [Leaning Time-Varying Instruments for Identifying Causal Effects in Time-Series Data](https://mlsanity.com/paper/2411.17774/) (2024)
- [Conditional Front-door Adjustment for Heterogeneous Treatment Assignment Effect Estimation Under Non-adherence](https://mlsanity.com/paper/2505.05677/) (2025)
- [Front-door Reducibility: Reducing ADMGs to the Standard Front-door Setting via a Graphical Criterion](https://mlsanity.com/paper/2511.15679/) (2025)
- [PIPCFR: Pseudo-outcome Imputation with Post-treatment Variables for Individual Treatment Effect Estimation](https://mlsanity.com/paper/2512.18737/) (2025)
- [CGRL: Causal-Guided Representation Learning for Node-Level Out-of-Distribution Generalization](https://mlsanity.com/paper/2603.24304/) (2026)
- [Prototype-Enhanced Multi-View Learning for Thyroid Nodule Ultrasound Classification](https://mlsanity.com/paper/2603.28315/) (2026)
- [Observable Neural ODEs for Identifiable Causal Forecasting in Continuous Time](https://mlsanity.com/paper/2604.26070/) (2026)
- [Uncertainty-Guided LLM Semantic Augmentation for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2607.26599/) (2026)

## Abstract (arXiv)

An essential and challenging problem in causal inference is causal effect estimation from observational data. The problem becomes more difficult with the presence of unobserved confounding variables. The front-door adjustment is a practical approach for dealing with unobserved confounding variables. However, the restriction for the standard front-door adjustment is difficult to satisfy in practice. In this paper, we relax some of the restrictions by proposing the concept of conditional front-door (CFD) adjustment and develop the theorem that guarantees the causal effect identifiability of CFD adjustment. Furthermore, as it is often impossible for a CFD variable to be given in practice, it is desirable to learn it from data. By leveraging the ability of deep generative models, we propose CFDiVAE to learn the representation of the CFD adjustment variable directly from data with the identifiable Variational AutoEncoder and formally prove the model identifiability. Extensive experiments on synthetic datasets validate the effectiveness of CFDiVAE and its superiority over existing methods. The experiments also show that the performance of CFDiVAE is less sensitive to the causal strength of unobserved confounding variables. We further apply CFDiVAE to a real-world dataset to demonstrate its potential application.