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1. Causal Effect Estimation with Mixed Latent Confounders and Post-treatment Variables

   Zhu, Yaochen; Ma, Jing; Wu, Liang; Guo, Qi; Hong, Liangjie; Li, Jundong (April 2025, International Conference on Learning Representations)

   Causal inference from observational data has attracted considerable attention among researchers. One main obstacle is the handling of confounders. As direct measurement of confounders may not be feasible, recent methods seek to address the confounding bias via proxy variables, i.e., covariates postulated to be conducive to the inference of latent confounders. However, the selected proxies may scramble both confounders and post-treatment variables in practice, which risks biasing the estimation by controlling for variables affected by the treatment. In this paper, we systematically investigate the bias due to latent post-treatment variables, i.e., latent post-treatment bias, in causal effect estimation. Specifically, we first derive the bias when selected proxies scramble both latent confounders and post-treatment variables, which we demonstrate can be arbitrarily bad. We then propose a Confounder-identifiable VAE (CiVAE) to address the bias. Based on a mild assumption that the prior of latent variables that generate the proxy belongs to a general exponential family with at least one invertible sufficient statistic in the factorized part, CiVAE individually identifies latent confounders and latent post-treatment variables up to bijective transformations. We then prove that with individual identification, the intractable disentanglement problem of latent confounders and post-treatment variables can be transformed into a tractable independence test problem despite arbitrary dependence may exist among them. Finally, we prove that the true causal effects can be unbiasedly estimated with transformed confounders inferred by CiVAE. Experiments on both simulated and real-world datasets demonstrate significantly improved robustness of CiVAE. 

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2. Multi-Cause Effect Estimation with Disentangled Confounder Representation

   https://doi.org/10.24963/ijcai.2021/384  

   Ma, Jing; Guo, Ruocheng; Zhang, Aidong; Li, Jundong (August 2021, Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence)

   null (Ed.)

   One fundamental problem in causality learning is to estimate the causal effects of one or multiple treatments (e.g., medicines in the prescription) on an important outcome (e.g., cure of a disease). One major challenge of causal effect estimation is the existence of unobserved confounders -- the unobserved variables that affect both the treatments and the outcome. Recent studies have shown that by modeling how instances are assigned with different treatments together, the patterns of unobserved confounders can be captured through their learned latent representations. However, the interpretability of the representations in these works is limited. In this paper, we focus on the multi-cause effect estimation problem from a new perspective by learning disentangled representations of confounders. The disentangled representations not only facilitate the treatment effect estimation but also strengthen the understanding of causality learning process. Experimental results on both synthetic and real-world datasets show the superiority of our proposed framework from different aspects. 

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3. Identifiability of causal effects with multiple causes and a binary outcome

   https://doi.org/10.1093/biomet/asab016  

   Kong, Dehan; Yang, Shu; Wang, Linbo (March 2021, Biometrika)

   Summary Unobserved confounding presents a major threat to causal inference in observational studies. Recently, several authors have suggested that this problem could be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that under a linear Gaussian model for the treatments, the causal effect is not identifiable without parametric assumptions on the outcome model. In this note, we show that the causal effect is indeed identifiable if we assume a general binary choice model for the outcome with a non-probit link. Our identification approach is based on the incongruence between Gaussianity of the treatments and latent confounder and non-Gaussianity of a latent outcome variable. We further develop a two-step likelihood-based estimation procedure. 

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4. Differentiable Cyclic Causal Discovery Under Unmeasured Confounders

   Sethuraman, Muralikrishnna G; Fekri, Faramarz (December 2025, 39th Conference on Neural Information Processing Systems (NeurIPS 2025))

   Understanding causal relationships between variables is fundamental across scientific disciplines. Most causal discovery algorithms rely on two key assump- tions: (i) all variables are observed, and (ii) the underlying causal graph is acyclic. While these assumptions simplify theoretical analysis, they are often violated in real-world systems, such as biological networks. Existing methods that account for confounders either assume linearity or struggle with scalability. To address these limitations, we propose DCCD-CONF, a novel framework for differentiable learning of nonlinear cyclic causal graphs in the presence of unmeasured confounders using interventional data. Our approach alternates between optimizing the graph structure and estimating the confounder distribution by maximizing the log-likelihood of the data. Through experiments on synthetic data and real-world gene perturbation datasets, we show that DCCD-CONF outperforms state-of-the-art methods in both causal graph recovery and confounder identification. Additionally, we provide consistency guarantees for our framework, reinforcing its theoretical soundness. 

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5. Propensity Score Weighting for Causal Inference with Clustered Data

   https://doi.org/10.1515/jci-2017-0027  

   Yang, Shu (September 2018, Journal of Causal Inference)

   Abstract Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania. 

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