# A Uniformly Consistent Estimator of Causal Effects under the k-Triangle-Faithfulness Assumption

arXiv: https://arxiv.org/abs/1502.00829 · HTML: https://mlsanity.com/paper/1502.00829/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2015.

## Built on by (most cited first, 10 of 10)

- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions](https://mlsanity.com/paper/2201.05666/) (2022)
- [Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Method](https://mlsanity.com/paper/2405.13100/) (2024)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Causal Discovery from Data Assisted by Large Language Models](https://mlsanity.com/paper/2503.13833/) (2025)
- [Efficient Latent Variable Causal Discovery: Combining Score Search and Targeted Testing](https://mlsanity.com/paper/2510.04263/) (2025)
- [A Uniformly Consistent Estimator of non-Gaussian Causal Effects Under the k-Triangle-Faithfulness Assumption](https://mlsanity.com/paper/2107.01333/) (2021)
- [Causal Razors](https://mlsanity.com/paper/2302.10331/) (2023)
- [MEC-IP: Efficient Discovery of Markov Equivalent Classes via Integer Programming](https://mlsanity.com/paper/2410.18147/) (2024)

## Abstract (arXiv)

Spirtes, Glymour and Scheines [Causation, Prediction, and Search (1993) Springer] described a pointwise consistent estimator of the Markov equivalence class of any causal structure that can be represented by a directed acyclic graph for any parametric family with a uniformly consistent test of conditional independence, under the Causal Markov and Causal Faithfulness assumptions. Robins et al. [Biometrika 90 (2003) 491-515], however, proved that there are no uniformly consistent estimators of Markov equivalence classes of causal structures under those assumptions. Subsequently, Kalisch and B"uhlmann [J. Mach. Learn. Res. 8 (2007) 613-636] described a uniformly consistent estimator of the Markov equivalence class of a linear Gaussian causal structure under the Causal Markov and Strong Causal Faithfulness assumptions. However, the Strong Faithfulness assumption may be false with high probability in many domains. We describe a uniformly consistent estimator of both the Markov equivalence class of a linear Gaussian causal structure and the identifiable structural coefficients in the Markov equivalence class under the Causal Markov assumption and the considerably weaker k-Triangle-Faithfulness assumption.