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Volumn 11, Issue 2, 2001, Pages 155-169

A hypergraph-theoretic analysis of collapsibility and decomposability for extended log-linear models

Author keywords

Acyclic hypergraphs; Collapsibility; Decomposability; Independence relation; Perfect decomposability; Total decomposability

Indexed keywords


EID: 0042379704     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008979300007     Document Type: Article
Times cited : (10)

References (44)
  • 2
    • 0000601361 scopus 로고
    • Collapsibility and response variables in contingency tables
    • Asmussen S. and Edwards D. 1983. Collapsibility and response variables in contingency tables. Biometrika 70: 367-378.
    • (1983) Biometrika , vol.70 , pp. 367-378
    • Asmussen, S.1    Edwards, D.2
  • 4
    • 0020782108 scopus 로고
    • On the desirability of acyclic database schemes
    • Beeri C., Fagin R., Maier D., and Yannakakis M. 1983. On the desirability of acyclic database schemes. J. of the ACM 29: 479-514.
    • (1983) J. of the ACM , vol.29 , pp. 479-514
    • Beeri, C.1    Fagin, R.2    Maier, D.3    Yannakakis, M.4
  • 5
    • 0003878763 scopus 로고
    • North-Holland, Amsterdam
    • Berge C. 1989. Hypergraphs. North-Holland, Amsterdam.
    • (1989) Hypergraphs
    • Berge, C.1
  • 7
    • 0000546609 scopus 로고
    • I-divergence geometry of probability distributions and minimization problems
    • Csiszar I. 1975. I-divergence geometry of probability distributions and minimization problems. Annals of Probability 3: 146-158.
    • (1975) Annals of Probability , vol.3 , pp. 146-158
    • Csiszar, I.1
  • 8
    • 0001637134 scopus 로고
    • Markov fields and log-linear interaction models for contigency tables
    • Darroch J.N., Lauritzen S.L., and Speed T.P. 1980. Markov fields and log-linear interaction models for contigency tables. Annals of Statistics 8: 522-539.
    • (1980) Annals of Statistics , vol.8 , pp. 522-539
    • Darroch, J.N.1    Lauritzen, S.L.2    Speed, T.P.3
  • 10
    • 0039447249 scopus 로고    scopus 로고
    • Characterization of decomposable dependency models
    • De Campos L.M. 1996. Characterization of decomposable dependency models. J. Artificial Intelligence Research 5: 289-300.
    • (1996) J. Artificial Intelligence Research , vol.5 , pp. 289-300
    • De Campos, L.M.1
  • 11
    • 0020781665 scopus 로고
    • Degrees of acyclicity for hypergraphs and relational database schemes
    • Fagin R. 1983. Degrees of acyclicity for hypergraphs and relational database schemes. J. ACM 30: 514-550.
    • (1983) J. ACM , vol.30 , pp. 514-550
    • Fagin, R.1
  • 12
    • 0000163612 scopus 로고
    • Marginalization and collapsibility in graphical interaction models
    • Frydenberg M. 1990. Marginalization and collapsibility in graphical interaction models. The Annals of Statistics 18: 790-805.
    • (1990) The Annals of Statistics , vol.18 , pp. 790-805
    • Frydenberg, M.1
  • 13
    • 0000279774 scopus 로고
    • Simultaneous test procedures: Some theory of multiple comparisons
    • Gabriel K.R. 1969. Simultaneous test procedures: Some theory of multiple comparisons. Ann. Math. Statist. 40: 224-250.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 224-250
    • Gabriel, K.R.1
  • 14
    • 21344496552 scopus 로고
    • Logical and algorithmic properties of conditional independence and graphical models
    • Geiger D. and Pearl J. 1993. Logical and algorithmic properties of conditional independence and graphical models. The Annals of Statistics 21: 2001-2021.
    • (1993) The Annals of Statistics , vol.21 , pp. 2001-2021
    • Geiger, D.1    Pearl, J.2
  • 15
    • 0042710614 scopus 로고
    • Decomposability and collapsibility for log-linear models
    • Geng Z. 1989. Decomposability and collapsibility for log-linear models. Algorithm AS 244. Appl. Statistics 38: 189-197.
    • (1989) Algorithm as 244. Appl. Statistics , vol.38 , pp. 189-197
    • Geng, Z.1
  • 21
    • 0001006209 scopus 로고
    • Local computations with probabilities on graphical structures and their application to expert systems
    • Lauritzen S.L. and Spiegelhalter D.J. 1988. Local computations with probabilities on graphical structures and their application to expert systems. J. of the Royal Statistical Society, Series B50: 157-224.
    • (1988) J. of the Royal Statistical Society, Series , vol.B50 , pp. 157-224
    • Lauritzen, S.L.1    Spiegelhalter, D.J.2
  • 22
    • 0002645829 scopus 로고
    • Optimal decompositions by clique-separators
    • Leimer H.-G. 1993. Optimal decompositions by clique-separators. Discrete Math. 113: 99-123.
    • (1993) Discrete Math. , vol.113 , pp. 99-123
    • Leimer, H.-G.1
  • 23
    • 0019544003 scopus 로고
    • Hierarchical schemata for relational databases
    • Lien Y.E. 1981. Hierarchical schemata for relational databases. ACM Transactions on Database Systems 6: 48-69.
    • (1981) ACM Transactions on Database Systems , vol.6 , pp. 48-69
    • Lien, Y.E.1
  • 24
    • 84976830370 scopus 로고
    • On the equivalence of database models
    • Lien Y.E. 1982. On the equivalence of database models. J. ACM 29: 333-362.
    • (1982) J. ACM , vol.29 , pp. 333-362
    • Lien, Y.E.1
  • 25
    • 0040076411 scopus 로고
    • An extension of the results of Asmussen and Edwards on collapsibility in contingency tables
    • Madigan D. and Mosurski K. 1990. An extension of the results of Asmussen and Edwards on collapsibility in contingency tables. Biometrika 77: 315-319.
    • (1990) Biometrika , vol.77 , pp. 315-319
    • Madigan, D.1    Mosurski, K.2
  • 26
    • 0021457287 scopus 로고
    • Connections in acyclic hypergraphs
    • Maier D. and Ullman J.D. 1984. Connections in acyclic hypergraphs. Theor. Comput. Sci. 32: 185-199.
    • (1984) Theor. Comput. Sci. , vol.32 , pp. 185-199
    • Maier, D.1    Ullman, J.D.2
  • 27
    • 38249028672 scopus 로고
    • Existence of extensions and product extensions for discrete probability distributions
    • Malvestuto F.M. 1988. Existence of extensions and product extensions for discrete probability distributions. Discrete Mathematics 69: 61-77.
    • (1988) Discrete Mathematics , vol.69 , pp. 61-77
    • Malvestuto, F.M.1
  • 28
    • 38249013365 scopus 로고
    • A unique formal system for binary decompositions of database relations, probability distributions, and graphs
    • Malvestuto F.M. 1992. A unique formal system for binary decompositions of database relations, probability distributions, and graphs, Information Sciences 59: 21-52; comment by Malvestuto F.M. and Studeny M. 1992. Information Sciences 63: 1-2.
    • (1992) Information Sciences , vol.59 , pp. 21-52
    • Malvestuto, F.M.1
  • 29
    • 44049112356 scopus 로고
    • Malvestuto F.M. 1992. A unique formal system for binary decompositions of database relations, probability distributions, and graphs, Information Sciences 59: 21-52; comment by Malvestuto F.M. and Studeny M. 1992. Information Sciences 63: 1-2.
    • (1992) Information Sciences , vol.63 , pp. 1-2
    • Malvestuto, F.M.1    Studeny, M.2
  • 30
    • 0042710611 scopus 로고
    • Recognizing submodels of loglinear hierarchical models
    • Dodge Y. and Whittaker J. (Eds.), (Proc. X Symp. on Computational Statistics), Physica Verlag, Heidelberg
    • Malvestuto F.M. 1992. Recognizing submodels of loglinear hierarchical models. In: Dodge Y. and Whittaker J. (Eds.), Computational Statistics, Vol. 1 (Proc. X Symp. on Computational Statistics), Physica Verlag, Heidelberg, pp. 263-267.
    • (1992) Computational Statistics , vol.1 , pp. 263-267
    • Malvestuto, F.M.1
  • 32
    • 0042710612 scopus 로고    scopus 로고
    • An axiomatization of loglinear models with an application to the model-search problem
    • Fisher D. and Lenz H.-J. (Eds.), Springer-Verlag, New York, 1
    • Malvestuto F.M. 1996a. An axiomatization of loglinear models with an application to the model-search problem. In: Fisher D. and Lenz H.-J. (Eds.), Lecture Notes in Statistics, Vol. 112, Springer-Verlag, New York, pp. 175-184.
    • (1996) Lecture Notes in Statistics , vol.112 , pp. 75-184
    • Malvestuto, F.M.1
  • 33
    • 21344465831 scopus 로고    scopus 로고
    • Testing implication of hierarchical log-linear models for discrete probability distributions
    • Malvestuto F.M. 1996b. Testing implication of hierarchical log-linear models for discrete probability distributions. Statistics and Computing 6: 169-176.
    • (1996) Statistics and Computing , vol.6 , pp. 169-176
    • Malvestuto, F.M.1
  • 34
    • 0003490684 scopus 로고    scopus 로고
    • Computing marginals in graphical models
    • Wegman F.J. and Azen S.P. (Eds.), Proc. of the II World Congress of the IASC, Pasadena, CA
    • Malvestuto F.M. 1997. Computing marginals in graphical models. In: Wegman F.J. and Azen S.P. (Eds.), Computing Science and Statistics, Vol. 29(2), Proc. of the II World Congress of the IASC, Pasadena, CA, pp. 52-58.
    • (1997) Computing Science and Statistics , vol.29 , Issue.2 , pp. 52-58
    • Malvestuto, F.M.1
  • 36
    • 0032203476 scopus 로고    scopus 로고
    • A complete axiomatization of full acyclic join dependencies
    • Malvestuto F.M. 1998b. A complete axiomatization of full acyclic join dependencies. Information Processing Letters 68: 133-139.
    • (1998) Information Processing Letters , vol.68 , pp. 133-139
    • Malvestuto, F.M.1
  • 37
    • 0032089769 scopus 로고    scopus 로고
    • A fast algorithm for query optimization in universal-relation databases
    • Malvestuto F.M. and Moscarini M. 1998. A fast algorithm for query optimization in universal-relation databases. J. of Computer & System Sciences 56: 299-309.
    • (1998) J. of Computer & System Sciences , vol.56 , pp. 299-309
    • Malvestuto, F.M.1    Moscarini, M.2
  • 38
    • 0042209519 scopus 로고    scopus 로고
    • Decomposition of a hypergraph by partial-edge separators
    • Malvestuto F.M. and Moscarini M. 2000. Decomposition of a hypergraph by partial-edge separators. Theoretical Computer Science 237:1-2: 57-79.
    • (2000) Theoretical Computer Science , vol.237 , pp. 1-2
    • Malvestuto, F.M.1    Moscarini, M.2
  • 39
    • 84986506326 scopus 로고
    • On the tree representation of chordal graphs
    • Shibata Y. 1988. On the tree representation of chordal graphs. J. of Graph Theory 12: 421-428.
    • (1988) J. of Graph Theory , vol.12 , pp. 421-428
    • Shibata, Y.1
  • 40
    • 0000455611 scopus 로고
    • Decompositions by clique separators
    • Tarjan R.E. 1985. Decompositions by clique separators. Discrete Mathematics 55: 221-232.
    • (1985) Discrete Mathematics , vol.55 , pp. 221-232
    • Tarjan, R.E.1
  • 41
    • 0021473698 scopus 로고
    • Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs
    • Tarjan R.E. and Yannakakis M. 1984. Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Computing 13: 566-591.
    • (1984) SIAM J. Computing , vol.13 , pp. 566-591
    • Tarjan, R.E.1    Yannakakis, M.2
  • 43
    • 0017129474 scopus 로고
    • Model search among multiplicative models
    • Wermuth N. 1976. Model search among multiplicative models. Biometrics 32: 253-263.
    • (1976) Biometrics , vol.32 , pp. 253-263
    • Wermuth, N.1
  • 44
    • 0002463920 scopus 로고
    • Computing the minimum fill-in is NP-complete
    • Yannakakis M. 1981. Computing the minimum fill-in is NP-complete. SIAM J. Alg. Disc. Math. 2: 77-79.
    • (1981) SIAM J. Alg. Disc. Math. , vol.2 , pp. 77-79
    • Yannakakis, M.1


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