Automating the Selection of Proxy Variables of Unmeasured Confounders
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Abstract (arXiv)
Recently, interest has grown in the use of proxy variables of unobserved confounding for inferring the causal effect in the presence of unmeasured confounders from observational data. One difficulty inhibiting the practical use is finding valid proxy variables of unobserved confounding to a target causal effect of interest. These proxy variables are typically justified by background knowledge. In this paper, we investigate the estimation of causal effects among multiple treatments and a single outcome, all of which are affected by unmeasured confounders, within a linear causal model, without prior knowledge of the validity of proxy variables. To be more specific, we first extend the existing proxy variable estimator, originally addressing a single unmeasured confounder, to accommodate scenarios where multiple unmeasured confounders exist between the treatments and the outcome. Subsequently, we present two different sets of precise identifiability conditions for selecting valid proxy variables of unmeasured confounders, based on the second-order statistics and higher-order statistics of the data, respectively. Moreover, we propose two data-driven methods for the selection of proxy variables and for the unbiased estimation of causal effects. Theoretical analysis demonstrates the correctness of our proposed algorithms. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 26 of its 82 references that are in the map. First posted on arXiv 25 May 2024.
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26 of 82 references.
References · 26
- 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
- 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
- 2018The Blessings of Multiple Causescited by 104
- 2020An Introduction to Proximal Causal Learningcited by 95
- 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 55
- 2022Latent Hierarchical Causal Structure Discovery with Rank Constraintscited by 51
- 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 40
- 2019Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variablescited by 39
- 2018A confounding bridge approach for double negative control inference on causal effectscited by 36
- 2016Large-Scale Kernel Methods for Independence Testingcited by 32
- 2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 28
- 2013On the Testability of Causal Models with Latent and Instrumental Variablescited by 26
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- 2018High-Dimensional Causal Discovery Under non-Gaussianitycited by 24
- 2014Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomizationcited by 22
- 2018Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Frameworkcited by 16
- 2019Comment on "Blessings of Multiple Causes"cited by 16
- 2020A Selective Review of Negative Control Methods in Epidemiologycited by 16
- 2020Identifying effects of multiple treatments in the presence of unmeasured confoundingcited by 16
- 2013Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Modelscited by 12
- 2021The Proximal ID Algorithmcited by 11
- 2023Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variablescited by 11
- 2013Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomicscited by 9
- 2022Discovering Ancestral Instrumental Variables for Causal Inference from Observational Datacited by 7
- 2015Confounder Adjustment in Multiple Hypothesis Testingcited by 6
- 2021Learning linear non-Gaussian directed acyclic graph with diverging number of nodescited by 6
- 2022Data-driven Automated Negative Control Estimation (DANCE): Search for, Validation of, and Causal Inference with Negative Controlscited by 2
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Citing papers per year: 2026: 2.
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