# Interaction Information for Causal Inference: The Case of Directed Triangle

arXiv: https://arxiv.org/abs/1701.08868 · HTML: https://mlsanity.com/paper/1701.08868/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2017.

## Built on by (most cited first, 7 of 7)

- [Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework](https://mlsanity.com/paper/2302.12247/) (2023)
- [Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applications](https://mlsanity.com/paper/2306.04539/) (2023)
- [Entropic Causal Inference: Identifiability and Finite Sample Results](https://mlsanity.com/paper/2101.03501/) (2021)
- [C-PMI: Conditional Pointwise Mutual Information for Turn-level Dialogue Evaluation](https://mlsanity.com/paper/2306.15245/) (2023)
- [Entropic Causal Inference: Graph Identifiability](https://mlsanity.com/paper/2509.16463/) (2025)
- [Conditional Dependence via U-Statistics Pruning](https://mlsanity.com/paper/2410.15888/) (2024)
- [Factorization Regret mediates compositional generalization in latent space](https://mlsanity.com/paper/2603.27134/) (2026)

## Abstract (arXiv)

Interaction information is one of the multivariate generalizations of mutual information, which expresses the amount information shared among a set of variables, beyond the information, which is shared in any proper subset of those variables. Unlike (conditional) mutual information, which is always non-negative, interaction information can be negative. We utilize this property to find the direction of causal influences among variables in a triangle topology under some mild assumptions.