The Inflation Technique Completely Solves the Causal Compatibility Problem

@article{Navascus2017TheIT,
  title={The Inflation Technique Completely Solves the Causal Compatibility Problem},
  author={Miguel Navascu{\'e}s and Elie Wolfe},
  journal={Journal of Causal Inference},
  year={2017},
  volume={8},
  pages={70 - 91}
}
Abstract The causal compatibility question asks whether a given causal structure graph — possibly involving latent variables — constitutes a genuinely plausible causal explanation for a given probability distribution over the graph’s observed categorical variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suffer from false negatives, i.e. they admit incompatible distributions as apparently compatible with the given graph. In 10.1515/jci-2017-0020… 
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References

SHOWING 1-10 OF 98 REFERENCES
The Inflation Technique for Causal Inference with Latent Variables
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
Causal compatibility inequalities admitting quantum violations in the triangle structure
It has long been recognized that certain quantum correlations are incompatible with particular assumption about classical causal structure. Given a causal structure of unknown classicality, the
Which causal structures might support a quantum-classical gap?
TLDR
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 entropic approach to causal correlations.
TLDR
This paper studies causal correlations from an entropic perspective, and shows how to use this framework to derive entropics causal inequalities.
Inferring latent structures via information inequalities
TLDR
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.
Causal discovery and inference: concepts and recent methodological advances
TLDR
The constraint-based approach to causal discovery, which relies on the conditional independence relationships in the data, is presented, and the assumptions underlying its validity are discussed.
Causal structures from entropic information: geometry and novel scenarios
TLDR
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.
Analysing causal structures with entropy
  • M. Weilenmann, R. Colbeck
  • Computer Science
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2017
TLDR
This work brings together the key aspects of these entropic techniques with unified terminology, filling several gaps and establishing new connections, all illustrated with examples.
Theory-independent limits on correlations from generalized Bayesian networks
TLDR
This work generalizes the formalism of classical Bayesian networks in order to investigate non-classical correlations in arbitrary causal structures, and finds that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes.
Information-theoretic inference of common ancestors
TLDR
This work proves an information-theoretic inequality that allows for the inference of common ancestors of observed parts in any DAG representing some unknown larger system and shows that a large amount of dependence in terms of mutual information among the observations implies the existence of a common ancestor that distributes this information.
...
...