Discriminating between causal structures in Bayesian Networks given partial observations

Philipp Moritz; Jörg Reichardt; Nihat Ay

Kybernetika (2014)

  • Volume: 50, Issue: 2, page 284-295
  • ISSN: 0023-5954

Abstract

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Given a fixed dependency graph G that describes a Bayesian network of binary variables X 1 , ⋯ , X n , our main result is a tight bound on the mutual information I c ( Y 1 , ⋯ , Y k ) = ∑ j = 1 k H ( Y j ) / c - H ( Y 1 , ⋯ , Y k ) of an observed subset Y 1 , ⋯ , Y k of the variables X 1 , ⋯ , X n . Our bound depends on certain quantities that can be computed from the connective structure of the nodes in G . Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.

How to cite

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Moritz, Philipp, Reichardt, Jörg, and Ay, Nihat. "Discriminating between causal structures in Bayesian Networks given partial observations." Kybernetika 50.2 (2014): 284-295. <http://eudml.org/doc/261858>.

@article{Moritz2014,
abstract = {Given a fixed dependency graph $G$ that describes a Bayesian network of binary variables $X_1, \dots , X_n$, our main result is a tight bound on the mutual information $I_c(Y_1, \dots , Y_k) = \sum _\{j=1\}^k H(Y_j)/c - H(Y_1, \dots , Y_k)$ of an observed subset $Y_1, \dots , Y_k$ of the variables $X_1, \dots , X_n$. Our bound depends on certain quantities that can be computed from the connective structure of the nodes in $G$. Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.},
author = {Moritz, Philipp, Reichardt, Jörg, Ay, Nihat},
journal = {Kybernetika},
keywords = {Bayesian networks; causal Markov condition; information theory; information inequalities; common ancestors; causal inference; Bayesian networks; causal Markov condition; information theory; information inequalities; common ancestors; causal inference},
language = {eng},
number = {2},
pages = {284-295},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Discriminating between causal structures in Bayesian Networks given partial observations},
url = {http://eudml.org/doc/261858},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Moritz, Philipp
AU - Reichardt, Jörg
AU - Ay, Nihat
TI - Discriminating between causal structures in Bayesian Networks given partial observations
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 2
SP - 284
EP - 295
AB - Given a fixed dependency graph $G$ that describes a Bayesian network of binary variables $X_1, \dots , X_n$, our main result is a tight bound on the mutual information $I_c(Y_1, \dots , Y_k) = \sum _{j=1}^k H(Y_j)/c - H(Y_1, \dots , Y_k)$ of an observed subset $Y_1, \dots , Y_k$ of the variables $X_1, \dots , X_n$. Our bound depends on certain quantities that can be computed from the connective structure of the nodes in $G$. Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.
LA - eng
KW - Bayesian networks; causal Markov condition; information theory; information inequalities; common ancestors; causal inference; Bayesian networks; causal Markov condition; information theory; information inequalities; common ancestors; causal inference
UR - http://eudml.org/doc/261858
ER -

References

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  1. Allman, E. S., Rhodes, J. A., Reconstructing Evolution: New Mathematical and Computational Advances, chapter Phylogenetic invariants., Oxford University Press, 2007. MR2307988
  2. Ay, N., 10.1016/j.dam.2008.06.032, Discrete Appl. Math. 157 (2009), 10, 2439-2457. MR2527961DOI10.1016/j.dam.2008.06.032
  3. Bollobás, B., Random Graphs., Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2001. Zbl1220.05117MR1864966
  4. Cover, T. M., Thomas, J. A., Elements of Information Theory. Second edition., Wiley, 2006. MR2239987
  5. Friedman, N., 10.1126/science.1094068, Science 303 (2004), 5659, 799-805. DOI10.1126/science.1094068
  6. Peters, J., Mooij, J., Janzing, D., Schölkopf, B., Causal discovery with continuous additive noise models., arXiv 1309.6779 (2013). 
  7. Lauritzen, S. L., Graphical Models., Oxford Science Publications, Clarendon Press, 1996. MR1419991
  8. Lauritzen, S. L., Sheehan, N. A., 10.1214/ss/1081443232, Statist. Sci. 18 (2003), 489-514. Zbl1055.62126MR2059327DOI10.1214/ss/1081443232
  9. Pearl, J., Causality: Models, Reasoning and Inference., Cambridge University Press, 2000. Zbl1188.68291MR1744773
  10. Reichenbach, H., Reichenbach, M., The Direction of Time., California Library Reprint Series, University of California Press, 1956. 
  11. Socolar, J. E. S., Kauffman, S. A., 10.1103/PhysRevLett.90.068702, Phys. Rev. Lett. 90 (2003), 068702. DOI10.1103/PhysRevLett.90.068702
  12. Steudel, B., Ay, N., Information-theoretic inference of common ancestors., CoRR, abs/1010.5720, 2010. 
  13. Studený, M., Probabilistic Conditional Independence Structures., Information Science and Statistics. Springer, 2005. Zbl1070.62001

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