# Comparing Two Proxy Methods for Causal Identification

arXiv: https://arxiv.org/abs/2512.00175 · HTML: https://mlsanity.com/paper/2512.00175/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [On the definition of a confounder](https://mlsanity.com/paper/1304.0564/) (2013)
- [Stochastic Gradients for Large-Scale Tensor Decomposition](https://mlsanity.com/paper/1906.01687/) (2019)
- [Causal Inference with Hidden Mediators](https://mlsanity.com/paper/2111.02927/) (2021)
- [Causal Inference with a Hidden Treatment](https://mlsanity.com/paper/2405.09080/) (2024)

## Built on by (most cited first, 2 of 2)

- [Identifying Causal Effects Using a Single Proxy Variable](https://mlsanity.com/paper/2604.09135/) (2026)
- [The Spectral Structure of Latent Treatment Effects](https://mlsanity.com/paper/2607.10926/) (2026)

## Abstract (arXiv)

Identifying causal effects in the presence of unmeasured variables is a fundamental challenge in causal inference, for which proxy variable methods have emerged as a powerful solution. We contrast two major approaches in this framework: (1) bridge equation methods, which leverage solutions to integral equations to recover causal targets, and (2) array decomposition methods, which recover latent factors used to identify counterfactual quantities via eigendecomposition tasks. We compare the model restrictions underlying these two approaches and provide insight into implications of the underlying assumptions, clarifying the scope of applicability for each method.