# Inferring latent structures via information inequalities

arXiv: https://arxiv.org/abs/1407.2256 · HTML: https://mlsanity.com/paper/1407.2256/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2014.

## Built on by (most cited first, 6 of 6)

- [Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables](https://mlsanity.com/paper/2107.07087/) (2021)
- [Bounding probabilities of causation through the causal marginal problem](https://mlsanity.com/paper/2304.02023/) (2023)
- [Causal Networks and Freedom of Choice in Bell's Theorem](https://mlsanity.com/paper/2105.05721/) (2021)
- [Restricted Hidden Cardinality Constraints in Causal Models](https://mlsanity.com/paper/2109.05656/) (2021)
- [Quantum causal inference in the presence of hidden common causes: An entropic approach](https://mlsanity.com/paper/2104.13227/) (2021)
- [Causal inference with imperfect instrumental variables](https://mlsanity.com/paper/2111.03029/) (2021)

## Abstract (arXiv)

One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial constraints on the observed distribution. Here, we propose an information-theoretic approach, based on the insight that conditions on entropies of Bayesian networks take the form of simple linear inequalities. We describe an algorithm for deriving entropic tests for latent structures. The well-known conditional independence tests appear as a special case. While the approach applies for generic Bayesian networks, we presently adopt the causal view, and show the versatility of the framework by treating several relevant problems from that domain: detecting common ancestors, quantifying the strength of causal influence, and inferring the direction of causation from two-variable marginals.