Algebraic causality : Bayes nets and beyond
Riccomagno, Eva and Smith, J. Q., 1953- (2007) Algebraic causality : Bayes nets and beyond. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
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The relationship between algebraic geometry and the inferential framework of the Bayesian Networks with hidden variables has now been fruitfully explored and exploited by a number of authors. More recently the algebraic formulation of Causal Bayesian Networks has also been investigated in this context. After reviewing these newer relationships, we proceed to demonstrate that many of the ideas embodied in the concept of a "causal model" can be more generally expressed directly in terms of a partial order and a family of polynomial maps. The more conventional graphical constructions, when available, remain a powerful tool.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Geometry, Algebraic, Statistics -- Graphic methods|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||22|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Restricted or Subscription Access|
|References:|| P.E. Anderson and J.Q. Smith A graphical framework for representing the semantics of asymmetric models quantifier elimination for statistical problems, CRiSM Tec.Rep 05-12, University of Warwick, 2005.  CoCoATeam, CoCoA: a system for doing Computations in Commutative Algebra, Available at http://cocoa.dima.unige.it.  R.G.Cowell, A.P. Dawid,S.L. Lauritzen and D.J.Spiegelhalter, Probabilistic Networks and Expert Systems, Springer, 1999.  A.P. Dawid Influence Diagrams for Causal Modelling and Inference, International Statistical Reviews 70: 161-89, 2002.  A.P. Dawid and M. Studen´y, Conditional products: an alternative approach to conditional independence, Artificial Intelligence and Statistics 99 (D. Heckerman and J. Whittaker, eds), Morgan Kauffman, 32-40, 1999.  M. Drton and S. Sullivant Algebraic statistical models, arXiv:math/0703609v1, 2007.  N. Freidman and M. Goldszmidt, Learning Bayesian networks with local structure, in M.I.Jordan, ed Learning in Graphical Models MIT Press 421 -459, 1999.  L.D. Garcia, M. Stillman and B. Sturmfels, Algebraic geometry of Bayesian networks, Journal of Symbolic Computation, 39(3-4):331-355, 2005.  D. Geiger, C. Meek and B. Sturmfels, On the toric algebra of graphical models, Ann. Statist. 34(3) 1463–1492, 2006.  M. Kuroki, Graphical identifiability criteria for causal effects in studies with an unobserved treatment/response variable, Biometrika 94(1) 37–47, 2007.  S.L. Lauritzen, Graphical Models, Clarendon Press, Oxford, 1996.  D. McAllister, M. Collins and F. Periera, Case Factor Diagrams for Structured Probability Modelling, In the Proceedings of the 20th Annual Conference on Uncertainty in Artificial Intelligence (UAI -04) 382-391.  D.M.Q. Mond, J.Q. Smith and D. Van Straten, Stochastic factorisations, sandwiched simplices and the topology of the space of explanations, Proc. R. Soc. London. A 459: 2821-2845, 2003.  L. Pachter and B. Sturmfels (eds.), Algebraic statistics for computational biology, Cambridge Univ. Press, New York, 2005.  J. Pearl, Causality. models, reasoning and inference, Cambridge University Press, Cambridge, 2000.  Statistics and Causal Inference: A Review (with discussion), Test, 12(2) 281-345, 2003.  G. Pistone, E. Riccomagno and H.P. Wynn, Algebraic Statistics, Chapman & Hall/CRC, Boca Raton, 2001.  D. Poole and N.L. Zhang, Exploiting Contextual Independence Probabilistic Inference Journal of Artificial Intelligence Research 18 263 -313, 2003.  E. Riccomagno and J.Q. Smith, Identifying a cause in models which are not simple Bayesian networks, Proceedings of IMPU, Perugia July 04, 1315-22, 2004.  , The Causal Manipulation of Chain Event Graphs, (submitted to The Annals of Statistics, 2007. CRiSM report n. 05-16).  , The geometry of causal probability trees that are algebraically constrained, Search for Optimality in Design and Statistics: Algebraic and Dynamical System Methods (L Pronzato and A A Zigljavsky eds.) Springer-Verlag, 95–129 (to appear).  A. Salmaron, A. Cano and S. Moral, Importance Sampling in Bayesian Networks using probability trees, Computational Statistics and Data Analysis 24 387 - 413, 2000.  R. Settimi and J.Q. Smith, Geometry, moments and conditional independence trees with hidden variables, The Annals of Statistics, 28(4):1179-1205, 2000.  G. Shafer, The Art of Causal Conjecture, Cambridge, MA, MIT Press, 2003.  J.Q. Smith and P.E. Anderson, Conditional independence and Chain event graphs, Artificial Intelligence, to appear, 2007.  P. Spirtes, C. Glymour and R. Scheines, Causation, Prediction, and Search, Springer-Verlag, New York, 1993.  S. Sullivant, Algebraic geometry of Gaussian Bayesian networks, http://www.citebase.org/abstract?id=oai:arXiv.org:0704.0918, 2007.  P.A. Thwaites and J.Q. Smith, Non-symmetric models, Chain Event graphs and Propagation, Proceedings of IPMU 2339 - 2347, 2006.  , Evaluating Causal Effects using Chain Event Graphs, Proceedings of the third Workshop on Probabilistic Graphical Models, Prague, 291-300, 2006.|
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