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Identifying Causal Effects Using a Single Proxy Variable

arXiv 2604.09135 ↗First posted 10 Apr 2026stat.ML cs.LG math.STcited by 0

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Abstract (arXiv)

Unobserved confounding is a key challenge when estimating causal effects from a treatment on an outcome. In this work, we assume that we observe a single, potentially multi-dimensional proxy variable of the unobserved confounder and that we know the mechanism that generates the proxy from the confounder. Under an assumption called Single Proxy Identifiability of Causal Effects or simply SPICE, we prove that this error mechanism is complete and causal effects are identifiable. We extend the proxy-based causal identifiability results by Kuroki and Pearl (2014); Pearl (2010) to multi-dimensional continuous settings, more flexible functional relationships and a broader class of distributions. Further, we develop a neural network based estimation framework, SPICE-Net, to estimate causal effects, which is applicable to both discrete and continuous treatments.

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References · 17

  1. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
  2. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 410
  3. 2020A Survey on Causal Inferencecited by 202
  4. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
  5. 2016Foundations of Structural Causal Models with Cycles and Latent Variablescited by 134
  6. 2015External Validity: From Do-Calculus to Transportability Across Populationscited by 75
  7. 2023Engression: Extrapolation through the Lens of Distributional Regressioncited by 51
  8. 2022A Survey of Deep Causal Models and Their Industrial Applicationscited by 10
  9. 2014Characteristic Kernels and Infinitely Divisible Distributionscited by 7
  10. 2023Kernel Single Proxy Control for Deterministic Confoundingcited by 5
  11. 2023Single Proxy Controlcited by 4
  12. 2022Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programmingcited by 3
5 more
  1. 2021Accessible Color Sequences for Data Visualizationcited by 2
  2. 2024Nonparametric Inference on Dose-Response Curves Without the Positivity Conditioncited by 2
  3. 2025Comparing Two Proxy Methods for Causal Identificationcited by 2
  4. 2025Detecting clinician implicit biases in diagnoses using proximal causal inferencecited by 1
  5. 2025Demystifying Proximal Causal Inferencecited by 1

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