# Identifying Causal Effects Using a Single Proxy Variable

arXiv: https://arxiv.org/abs/2604.09135 · HTML: https://mlsanity.com/paper/2604.09135/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 65 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 17 of 17)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [A Survey of Deep Causal Models and Their Industrial Applications](https://mlsanity.com/paper/2209.08860/) (2022)
- [Characteristic Kernels and Infinitely Divisible Distributions](https://mlsanity.com/paper/1403.7304/) (2014)
- [Kernel Single Proxy Control for Deterministic Confounding](https://mlsanity.com/paper/2308.04585/) (2023)
- [Single Proxy Control](https://mlsanity.com/paper/2302.06054/) (2023)
- [Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming](https://mlsanity.com/paper/2210.09885/) (2022)
- [Accessible Color Sequences for Data Visualization](https://mlsanity.com/paper/2107.02270/) (2021)
- [Nonparametric Inference on Dose-Response Curves Without the Positivity Condition](https://mlsanity.com/paper/2405.09003/) (2024)
- [Comparing Two Proxy Methods for Causal Identification](https://mlsanity.com/paper/2512.00175/) (2025)
- [Detecting clinician implicit biases in diagnoses using proximal causal inference](https://mlsanity.com/paper/2501.16399/) (2025)
- [Demystifying Proximal Causal Inference](https://mlsanity.com/paper/2512.24413/) (2025)

## 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.