# Robust Weighted Triangulation of Causal Effects Under Model Uncertainty

arXiv: https://arxiv.org/abs/2603.01119 · HTML: https://mlsanity.com/paper/2603.01119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 61 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization](https://mlsanity.com/paper/1401.5755/) (2014)
- [A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects](https://mlsanity.com/paper/1903.03662/) (2019)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)
- [Post-selection inference for causal effects after causal discovery](https://mlsanity.com/paper/2405.06763/) (2024)
- [On the Hardness of Conditional Independence Testing In Practice](https://mlsanity.com/paper/2512.14000/) (2025)
- [Estimation of Effects of Sequential Treatments by Reparameterizing Directed Acyclic Graphs](https://mlsanity.com/paper/1302.1566/) (2013)
- [Are Bayesian networks typically faithful?](https://mlsanity.com/paper/2410.16004/) (2024)
- [Causal Inference through a Witness Protection Program](https://mlsanity.com/paper/1406.0531/) (2014)
- [Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions](https://mlsanity.com/paper/2103.08195/) (2021)
- [Average Causal Effect Estimation in DAGs with Hidden Variables: Beyond Back-Door and Front-Door Criteria](https://mlsanity.com/paper/2409.03962/) (2024)
- [Statistical and Causal Robustness for Causal Null Hypothesis Tests](https://mlsanity.com/paper/2310.10393/) (2023)
- [Adaptive Proximal Causal Inference with Some Invalid Proxies](https://mlsanity.com/paper/2507.19623/) (2025)
- [Automating the Selection of Proxy Variables of Unmeasured Confounders](https://mlsanity.com/paper/2405.16130/) (2024)
- [On doubly robust estimation for logistic partially linear models](https://mlsanity.com/paper/1901.09138/) (2019)
- [Bayesian Model Averaging in Causal Instrumental Variable Models](https://mlsanity.com/paper/2504.13520/) (2025)

## Built on by (most cited first, 1 of 1)

- [Multi-Method Causal Evidence Synthesis: Ranking Candidate Drivers by Convergent Cross-Method Evidence from Observational Data](https://mlsanity.com/paper/2608.20187/) (2026)

## Abstract (arXiv)

A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and possibly partially overlapping, sets of identifying assumptions to infer the causal effect, a process known as triangulation. Principled methods for triangulation, however, remain underdeveloped. Here, we develop a framework for causal effect triangulation that combines model testability methods from causal discovery with statistical inference methods from semiparametric theory, while avoiding explicit model selection and post-selection inference problems. We propose a triangulation functional that combines identified functionals from each model with data-driven measures of model validity. We provide a bound on the distance of the functional from the true causal effect along with conditions under which this distance can be taken to zero. Finally, we derive valid statistical inference for this functional. Our framework formalizes robustness under causal pluralism without requiring agreement across models or commitment to a single specification. We demonstrate its performance through simulations and an empirical application.