# A Weaker Faithfulness Assumption based on Triple Interactions

arXiv: https://arxiv.org/abs/2010.14265 · HTML: https://mlsanity.com/paper/2010.14265/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2020.

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

- [Ultra-marginal Feature Importance: Learning from Data with Causal Guarantees](https://mlsanity.com/paper/2204.09938/) (2022)
- [Causal discovery under a confounder blanket](https://mlsanity.com/paper/2205.05715/) (2022)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Exploiting Causal Graph Priors with Posterior Sampling for Reinforcement Learning](https://mlsanity.com/paper/2310.07518/) (2023)
- [CausalARC: Abstract Reasoning with Causal World Models](https://mlsanity.com/paper/2509.03636/) (2025)
- [Optimal estimation of Gaussian (poly)trees](https://mlsanity.com/paper/2402.06380/) (2024)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Optimal structure learning and conditional independence testing](https://mlsanity.com/paper/2507.05689/) (2025)
- [Information-theoretic signatures of causality in Bayesian networks and hypergraphs](https://mlsanity.com/paper/2512.20552/) (2025)
- [High-Order Markov Blanket Discovery via a k-Order Relaxation of the Faithfulness Assumption](https://mlsanity.com/paper/2607.26357/) (2026)

## Abstract (arXiv)

One of the core assumptions in causal discovery is the faithfulness assumption, i.e., assuming that independencies found in the data are due to separations in the true causal graph. This assumption can, however, be violated in many ways, including xor connections, deterministic functions or cancelling paths. In this work, we propose a weaker assumption that we call 2-adjacency faithfulness. In contrast to adjacency faithfulness, which assumes that there is no conditional independence between each pair of variables that are connected in the causal graph, we only require no conditional independence between a node and a subset of its Markov blanket that can contain up to two nodes. Equivalently, we adapt orientation faithfulness to this setting. We further propose a sound orientation rule for causal discovery that applies under weaker assumptions. As a proof of concept, we derive a modified Grow and Shrink algorithm that recovers the Markov blanket of a target node and prove its correctness under strictly weaker assumptions than the standard faithfulness assumption.