# Restricted Hidden Cardinality Constraints in Causal Models

arXiv: https://arxiv.org/abs/2109.05656 · HTML: https://mlsanity.com/paper/2109.05656/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 30 references that are in the map.
- First posted on arXiv 13 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Positive semidefinite rank](https://mlsanity.com/paper/1407.4095/) (2014)
- [Quantifier Elimination for Statistical Problems](https://mlsanity.com/paper/1301.6698/) (2013)
- [Inferring latent structures via information inequalities](https://mlsanity.com/paper/1407.2256/) (2014)
- [Inferring causal structure: a quantum advantage](https://mlsanity.com/paper/1406.5036/) (2014)

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

- [Causal Discovery in Mixtures of Populations](https://mlsanity.com/paper/2311.07454/) (2023)

## Abstract (arXiv)

Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without making additional assumptions about the model. In this work, we consider causal models with a promise that unobserved variables have known cardinalities. We derive inequality constraints implied by d-separation in such models. Moreover, we explore the possibility of leveraging this result to study causal influence in models that involve quantum systems.