Graphs for Margins of Bayesian Networks

Evans, Robin J.

doi:10.1111/sjos.12194

Cited by 59 publications

(73 citation statements)

References 33 publications

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“…As shown by Evans (see proposition 4.9(b) and theorem 4.13 in [17]), every GDAG is observationally equivalent to its canonical projection, in the sense that they have the same set of possible marginal distributions P (V ) on the observed variables.…”

Section: Definition 3: Hidden Paths and Causes Let X Ymentioning

confidence: 90%

“…We begin with some useful definitions adapted from [16,17]. Where our terminology differs from that of Evans, a translation is provided in the footnotes.…”

Section: The Skeleton Methods and E-separationmentioning

confidence: 99%

“…By definition, both have the same skeleton, shown in (c). This example is taken from Evans [17]. 1 Our connected subsets are Evans' bidirected faces.…”

Section: Definition 3: Hidden Paths and Causes Let X Ymentioning

confidence: 99%

“…Our set  ( ) V G is Evans' set  . Compare to Evans [17]. 2 Our procedure of canonical projection is, in Evan's language, equivalent to taking the canonical DAG of the latent projection over the unobserved nodes of the original GDAG.…”

Section: Definition 3: Hidden Paths and Causes Let X Ymentioning

confidence: 99%

“…Section 2 contains essential notation and background. We then show in section 3 that some simple graphical methods due to Evans [16,17] can be used to confirm the interestingness of a graph by inspection. To illustrate the usefulness of this method, we apply it to the graphs considered by HLP and confirm their results.…”

Section: Introductionmentioning

confidence: 99%

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Which causal structures might support a quantum–classical gap?

Pienaar¹

2017

New J. Phys.

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A causal scenario is a graph that describes the cause and effect relationships between all relevant variables in an experiment. A scenario is deemed 'not interesting' if there is no device-independent way to distinguish the predictions of classical physics from any generalised probabilistic theory (including quantum mechanics). Conversely, an interesting scenario is one in which there exists a gap between the predictions of different operational probabilistic theories, as occurs for example in Belltype experiments. Henson, Lal and Pusey (HLP) recently proposed a sufficient condition for a causal scenario to not be interesting. In this paper we supplement their analysis with some new techniques and results. We first show 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. For three exceptional cases-the graphs numbered #15, 16, 20 in HLP-we show that there exist non-Shannon type entropic inequalities that imply these graphs are interesting. In doing so, we find that existing methods of entropic inequalities can be greatly enhanced by conditioning on the specific values of certain variables. then we say that the observed phenomenon can be explained by the model. Hypothesis testing then becomes the work of designing experiments to rule out different competing explanations.The literature on causal inference provides numerous tools for deciding when one causal model is a better explanation than another. In general, simpler explanations are preferable to more complex ones. Explanations should be faithful, meaning (roughly) that the observed independencies appear in almost all causal models that have the same causal structure as the chosen explanation. If these principles are not enough to differentiate different hypotheses, it is always possible to do so by performing experimental interventions: actively changing the values of some variables and observing the reaction of the remaining variables. A tool of causal inference called the do-calculus tells us which interventions are needed to obtain specific information about the causal structure.The question arises as to whether certain experiments in quantum physics, particularly the so-called 'Belltype' experiments [4-6], can be explained by a causal model. It is widely agreed that any explanation of quantum phenomena in terms of a classical causal model must violate at least one of several assumptions that hold for purely classical phenomena. For example, a classical causal model can explain quantum phenomena if we allow causes to propagate faster than light, as in Bohmian mechanics [7], or if we allow measurement settings to be influenced by a hidden common cause (the super-determinism loophole), and there are many other options. A more recent perspective due to Wood and Spekkens is that classical causal explanations of quantum experiments cannot be faithful [8], i.e. the causal model is not a generic example of the set of models that share it...

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Section: Definition 3: Hidden Paths and Causes Let X Ymentioning

confidence: 90%

“…We begin with some useful definitions adapted from [16,17]. Where our terminology differs from that of Evans, a translation is provided in the footnotes.…”

Section: The Skeleton Methods and E-separationmentioning

confidence: 99%

“…By definition, both have the same skeleton, shown in (c). This example is taken from Evans [17]. 1 Our connected subsets are Evans' bidirected faces.…”

Section: Definition 3: Hidden Paths and Causes Let X Ymentioning

confidence: 99%

Section: Definition 3: Hidden Paths and Causes Let X Ymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Which causal structures might support a quantum–classical gap?

Pienaar¹

2017

New J. Phys.

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A Convergent Inflation Hierarchy for Quantum Causal Structures

Gachechiladze

Gross

2023

Commun. Math. Phys.

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A causal structure is a description of the functional dependencies between random variables. A distribution is compatible with a given causal structure if it can be realized by a process respecting these dependencies. Deciding whether a distribution is compatible with a structure is a practically and fundamentally relevant, yet very difficult problem. Only recently has a general class of algorithms been proposed: These so-called inflation techniques associate to any causal structure a hierarchy of increasingly strict compatibility tests, where each test can be formulated as a computationally efficient convex optimization problem. Remarkably, it has been shown that in the classical case, this hierarchy is complete in the sense that each non-compatible distribution will be detected at some level of the hierarchy. An inflation hierarchy has also been formulated for causal structures that allow for the observed classical random variables to arise from measurements on quantum states—however, no proof of completeness of this quantum inflation hierarchy has been supplied. In this paper, we construct a first version of the quantum inflation hierarchy that is provably convergent. It takes an additional parameter, r, which can be interpreted as an upper bound on the Schmidt rank of the observables involved. For each r, it provides a family of increasingly strict and ultimately complete compatibility tests for correlations that are compatible with a given causal structure under this Schmidt rank constraint. From a technical point of view, convergence proofs are built on de Finetti theorems, which show that certain symmetries (which can be imposed in convex optimization problems) imply independence of random variables (which is not directly a convex constraint). A main technical ingredient to our proof is a Quantum de Finetti Theorem that holds for general tensor products of $$C^*$$ C ∗ -algebras, generalizing previous work that was restricted to minimal tensor products.

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Causal Structure Learning: A Combinatorial Perspective

Squires

Uhler

2022

Found Comput Math

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In this review, we discuss approaches for learning causal structure from data, also called causal discovery. In particular, we focus on approaches for learning directed acyclic graphs and various generalizations which allow for some variables to be unobserved in the available data. We devote special attention to two fundamental combinatorial aspects of causal structure learning. First, we discuss the structure of the search space over causal graphs. Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can be refined by adding interventional data.

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Graphs for Margins of Bayesian Networks

Cited by 59 publications

References 33 publications

Which causal structures might support a quantum–classical gap?

Which causal structures might support a quantum–classical gap?

A Convergent Inflation Hierarchy for Quantum Causal Structures

Causal Structure Learning: A Combinatorial Perspective

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