# Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables

@inproceedings{Finkelstein2021EntropicIC, title={Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables}, author={Noam Finkelstein and Beata Zjawin and Elie Wolfe and Ilya Shpitser and Robert W. Spekkens}, booktitle={UAI}, year={2021} }

Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the distribution of observed variables. In this work, we present entropic inequality constraints that are implied by eseparation relations in hidden variable DAGs with discrete observed variables. The constraints can intuitively be understood to follow from the fact that…

## References

SHOWING 1-10 OF 39 REFERENCES

### Graphical methods for inequality constraints in marginalized DAGs

- Economics, Mathematics2012 IEEE International Workshop on Machine Learning for Signal Processing
- 2012

It is shown that the observed distribution of a discrete model is always restricted if any two observed variables are neither adjacent in the graph, nor share a latent parent; this generalizes the well known instrumental inequality.

### Causal structures from entropic information: geometry and novel scenarios

- Computer Science
- 2014

This paper treats Bell scenarios involving multiple parties and multiple observables per party, and exhibits inequalities for scenarios with extra conditional independence assumptions, as well as a limited amount of shared randomness between the parties.

### Nested Markov Properties for Acyclic Directed Mixed Graphs

- MathematicsUAI
- 2012

This work provides a graphical characterization of the constraints given in [5] via a nested Markov property that uses a 'fixing' transformation on graphs that shows that marginal distributions of DAG models obey this property.

### Exclusivity Graph Approach to Instrumental Inequalities

- Computer ScienceUAI
- 2019

This work applies a technique, originally developed in the field of quantum foundations, to express the constraints implied by causal relations in the language of graph theory and can be applied to any causal model containing a latent variable.

### Inferring latent structures via information inequalities

- Computer ScienceUAI
- 2014

An information-theoretic approach is proposed, based on the insight that conditions on entropies of Bayesian networks take the form of simple linear inequalities, and an algorithm for deriving entropic tests for latent structures is described.

### Equivalence and Synthesis of Causal Models

- Computer ScienceUAI
- 1990

The canonical representation presented here yields an efficient algorithm for determining when two embedded causal models reflect the same dependency information, which leads to a model theoretic definition of causation in terms of statistical dependencies.

### Which causal structures might support a quantum–classical gap?

- Computer Science
- 2017

It is shown that existing graphical techniques due to Evans can be used to confirm by inspection that many graphs are interesting without having to explicitly search for inequality violations, and that existing methods of entropic inequalities can be greatly enhanced by conditioning on the specific values of certain variables.

### The Inflation Technique for Causal Inference with Latent Variables

- EconomicsJournal of Causal Inference
- 2019

Abstract The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal…

### Differentiable Causal Discovery Under Unmeasured Confounding

- Computer ScienceAISTATS
- 2021

This work derives differentiable algebraic constraints that fully characterize the space of ancestral acyclic directed mixed graphs, as well as more general classes of ADMGs, arid AD MGs and bow-free ADMGS, that capture all equality restrictions on the observed variables.

### Ordering-Based Causal Structure Learning in the Presence of Latent Variables

- Computer ScienceAISTATS
- 2020

It is proved that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model, and a greedy algorithm is proposed over the space of posets for causal structure discovery in the presence of latent confounders.