# Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning

arXiv: https://arxiv.org/abs/2505.05192 · HTML: https://mlsanity.com/paper/2505.05192/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 22 of 22)

- [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)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [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)
- [On the role of surrogates in the efficient estimation of treatment effects with limited outcome data](https://mlsanity.com/paper/2003.12408/) (2020)
- [Subspace Identification for Multi-Source Domain Adaptation](https://mlsanity.com/paper/2310.04723/) (2023)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder](https://mlsanity.com/paper/2310.01937/) (2023)
- [Long-Term Effect Estimation with Surrogate Representation](https://mlsanity.com/paper/2008.08236/) (2020)
- [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)
- [β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap](https://mlsanity.com/paper/2110.05225/) (2021)
- [Identification and estimation of treatment effects on long-term outcomes in clinical trials with external observational data](https://mlsanity.com/paper/2208.10163/) (2022)
- [Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects](https://mlsanity.com/paper/2201.10743/) (2022)
- [Policy Learning for Balancing Short-Term and Long-Term Rewards](https://mlsanity.com/paper/2405.03329/) (2024)
- [Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights](https://mlsanity.com/paper/2406.19195/) (2024)
- [Nonparametric Heterogeneous Long-term Causal Effect Estimation via Data Combination](https://mlsanity.com/paper/2502.18960/) (2025)
- [Long-term Causal Inference via Modeling Sequential Latent Confounding](https://mlsanity.com/paper/2502.18994/) (2025)

## Built on by (most cited first, 3 of 3)

- [Causal View of Time Series Imputation: Some Identification Results on Missing Mechanism](https://mlsanity.com/paper/2505.07180/) (2025)
- [Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects](https://mlsanity.com/paper/2604.00915/) (2026)
- [Representation Learning for Sample-Efficient CATE Estimation by Leveraging Multiple Outcomes](https://mlsanity.com/paper/2609.06294/) (2026)

## Abstract (arXiv)

Estimating long-term causal effects by combining long-term observational and short-term experimental data is a crucial but challenging problem in many real-world scenarios. In existing methods, several ideal assumptions, e.g. latent unconfoundedness assumption or additive equi-confounding bias assumption, are proposed to address the latent confounder problem raised by the observational data. However, in real-world applications, these assumptions are typically violated which limits their practical effectiveness. In this paper, we tackle the problem of estimating the long-term individual causal effects without the aforementioned assumptions. Specifically, we propose to utilize the natural heterogeneity of data, such as data from multiple sources, to identify latent confounders, thereby significantly avoiding reliance on idealized assumptions. Practically, we devise a latent representation learning-based estimator of long-term causal effects. Theoretically, we establish the identifiability of latent confounders, with which we further achieve long-term effect identification. Extensive experimental studies, conducted on multiple synthetic and semi-synthetic datasets, demonstrate the effectiveness of our proposed method.