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Reading Dependencies from Polytree-Like Bayesian Networks [article]

Jose M. Pena
2012 arXiv   pre-print
We present a graphical criterion for reading dependencies from the minimal directed independence map G of a graphoid p when G is a polytree and p satisfies composition and weak transitivity.  ...  We prove that the criterion is sound and complete. We argue that assuming composition and weak transitivity is not too restrictive.  ...  Acknowledgements This work is funded by the Swedish Research Council (ref. VR-621-2005-4202) . We thank the three anony-mous referees for their comments.  ... 
arXiv:1206.5263v1 fatcat:n7ypxh2qc5hz3g3ej3mysbpmea

Reading Dependencies from Covariance Graphs [article]

Jose M. Peña
2012 arXiv   pre-print
In this paper, we present a graphical criterion for reading dependencies from G, under the assumption that p satisfies the graphoid properties as well as weak transitivity and composition.  ...  The covariance graph (aka bi-directed graph) of a probability distribution p is the undirected graph G where two nodes are adjacent iff their corresponding random variables are marginally dependent in  ...  We thank the anonymous reviewers and the editor for their thorough review of this manuscript.  ... 
arXiv:1010.4504v3 fatcat:74gwe7t5nnchljaqt7m3qomt4m

Faithfulness of Probability Distributions and Graphs [article]

Kayvan Sadeghi
2017 arXiv   pre-print
The main goal of this paper is to provide a theoretical answer to this problem. We work with general independence models, which contain probabilistic independence models as a special case.  ...  We present our results for the general case of mixed graphs, but specialize the definitions and results to the better-known subclasses of undirected (concentration) and bidirected (covariance) graphs as  ...  Acknowledgments The original idea of this paper was inspired by discussions at the American Institute of Mathematics workshop "Positivity, Graphical Models, and the Modeling of Complex Multivariate Dependencies  ... 
arXiv:1701.08366v2 fatcat:yvgu5zwzwrhptgar2g7yejwuhi

On Finite Exchangeability and Conditional Independence [article]

Kayvan Sadeghi
2020 arXiv   pre-print
We show that the independence structure of exchangeable random networks lies in one of six regimes that are two-fold dual to one another, represented by undirected and bidirected independence graphs in  ...  We study the independence structure of finitely exchangeable distributions over random vectors and random networks.  ...  Acknowledgements The author is grateful to Steffen Lauritzen and Alessandro Rinaldo for raising this problem in one of our numerous conversations.  ... 
arXiv:1907.02912v3 fatcat:7awh7qf3mvhavpnsje5onekjdq

On finite exchangeability and conditional independence

Kayvan Sadeghi
2020 Electronic Journal of Statistics  
We show that the independence structure of exchangeable random networks lies in one of six regimes that are two-fold dual to one another, represented by undirected and bidirected independence graphs in  ...  We study the independence structure of finitely exchangeable distributions over random vectors and random networks.  ...  Acknowledgements The author is grateful to Steffen Lauritzen and Alessandro Rinaldo for raising this problem in one of our numerous conversations.  ... 
doi:10.1214/20-ejs1730 fatcat:y2gwkb4rhfba3cqoefvtosjvs4

Generating Graphoids from Generalised Conditional Probability [article]

Nic Wilson
2013 arXiv   pre-print
We take a general approach to uncertainty on product spaces, and give sufficient conditions for the independence structures of uncertainty measures to satisfy graphoid properties.  ...  The conditions include a sufficient condition for the Intersection property which can still apply even if there is a strong logical relations hip between the variables.  ...  If Ip is a semi-graphoid, then a result in [Verma, 86] (also Theorem 9 of [Pearl, 88] ) implies that the Bound ary DAG is a minimal I-map for IP so that conditional independence properties of Ip can  ... 
arXiv:1302.6852v1 fatcat:fazyyq2zrreobhkrjgfqnbmqha

Generating Graphoids from Generalised Conditional Probability [chapter]

Nic Wilson
1994 Uncertainty Proceedings 1994  
We take a general approach to uncertainty on product spaces, and give sufficient conditions for the independence structures of uncertainty measures to satisfy graphoid properties.  ...  Since these conditions are arguably more intuitive than some of the graphoid properties, they can be viewed as explanations why probability and certain other formalisms generate graphoids.  ...  The author is supported by a SERC postdoctoral fellowship. I am also grateful for the use of the computing facilities of the school of Computing and Mathematical Sciences, Oxford Brookes University.  ... 
doi:10.1016/b978-1-55860-332-5.50079-1 fatcat:utcg67mvd5e7rfsw4ujyy42zga

Deriving a Minimal I-map of a Belief Network Relative to a Target Ordering of its Nodes [article]

Izhar Matzkevich, Bruce Abramson
2013 arXiv   pre-print
These results promise to have a significant impact on the derivation of consensus models, as well as on other algorithms that require the reconfiguration and/or combination of BN's.  ...  This paper identifies and solves a new optimization problem: Given a belief network (BN) and a target ordering on its variables, how can we efficiently derive its minimal I-map whose arcs are consistent  ...  Acknowledgement We thank Ross Shachter for the insight and a useful feedback on an earlier draft of this paper.  ... 
arXiv:1303.1473v1 fatcat:rw2oo6tupfe4ziip5mxvyfkd4y

Independency relationships and learning algorithms for singly connected networks

LUIS M. DE CAMPOS
1998 Journal of experimental and theoretical artificial intelligence (Print)  
Dependency models are called sem i-graphoids if they verify the axioms A 1± A4, and graphoids if they satisfy the axioms A1± A 5 (Pearl 1988).  ...  Given a dependency model, M , we say that an undirected graph (a dag, respectively), G, is an Independency map or I-m ap (Pearl 1988) if every separation (d-separation respectively) in G implies an independency  ...  I am especially grateful to Silvia Acid, for her invaluable help with the painstaking algorithm work. I am most obliged to Gregory Cooper for providing the Alarm database.  ... 
doi:10.1080/095281398146743 fatcat:xr254qv3w5apnatffzlfog2zua

Conditional Plausibility Measures and Bayesian Networks [article]

Joseph Y. Halpern
2014 arXiv   pre-print
It is shown that the technology of Bayesian networks can be applied to algebraic conditional plausibility measures.  ...  A general notion of algebraic conditional plausibility measures is defined.  ...  Acknowledgments I thank Seraffn Moral, Fabio Cozman, and the anonymous referees for very useful comments. This work was sup ported in part by the NSF, under grant IRI-96-25901.  ... 
arXiv:1407.7182v1 fatcat:icvd4oqkezfsbdwahxhujr7yoq

Conditional Plausibility Measures and Bayesian Networks

J. Y. Halpern
2001 The Journal of Artificial Intelligence Research  
A general notion of algebraic conditional plausibility measures is defined.  ...  Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining algebraic conditional plausibility measures  ...  Acknowledgments I thank Serafín Moral, Fabio Cozman, and the anonymous referees for very useful comments. This work was supported in part by the NSF, under grant IRI-96-25901.  ... 
doi:10.1613/jair.817 fatcat:qvyalv2ggveilkes6f6v35zeim

The geometry of Gaussian double Markovian distributions [article]

Tobias Boege, Thomas Kahle, Andreas Kretschmer, Frank Röttger
2021 arXiv   pre-print
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse.  ...  We study the semi-algebraic geometry of these models, in particular their dimension, smoothness and connectedness as well as algebraic and combinatorial properties.  ...  We also thank the organizers of the summer research project "Linear Spaces of Symmetric Matrices" at MPI MiS Leipzig, where this problem was first posed.  ... 
arXiv:2107.00134v2 fatcat:g7kfzzbe7nezzjjhmeqapeltkm

Transitional Conditional Independence [article]

Patrick Forré
2021 arXiv   pre-print
Transitional conditional independence is asymmetric in general and it will be shown that it satisfies all desired relevance relations in terms of left and right versions of the separoid rules, except symmetry  ...  We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables.  ...  This work was partially supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement n o 639466).  ... 
arXiv:2104.11547v2 fatcat:rq3yjhya7rfbtapf4ncwgd6rii

Causal inference using the algorithmic Markov condition [article]

Dominik Janzing, Bernhard Schoelkopf
2008 arXiv   pre-print
Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian.  ...  This can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions  ...  This is transitive since the concatenation of covariant maps is again covariant.  ... 
arXiv:0804.3678v1 fatcat:dlyvlt5hjvdzppplwldq7xtfgu

Causal Inference Using the Algorithmic Markov Condition

Dominik Janzing, Bernhard Scholkopf
2010 IEEE Transactions on Information Theory  
Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian.  ...  This can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions  ...  ACKNOWLEDGEMENTS The authors would like to thank Bastian Steudel for helpful comments.  ... 
doi:10.1109/tit.2010.2060095 fatcat:4ht3vz4h35fy7mlydr2tlcqdiy
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