[1] Asmussen, S., Edwards, D.:
Collapsibility and response variables in contingency tables. Biometrika 70 (1983), 367–378.
MR 0725370 |
Zbl 0549.62041
[2] Bacharach, M.:
Biproportional Matrices and Input-Output Change. Cambridge University Press, Cambridge 1970.
MR 0263409 |
Zbl 0195.49705
[3] Badsberg, J.-H., Malvestuto, F. M.:
An implementation of the iterative proportional fitting procedure by propagation trees. Comput. Statist. Data Analysis 37 (2001), 297–322.
MR 1856676 |
Zbl 1061.65500
[4] Beeri, C., Vardi, M.: On the Properties of Full Join Dependencies. Adv. Database Theory I, Plenum Press, New York 1981.
[5] Beeri, C., Fagin, R., Maier, D., Yannakakis, M.:
On the desirability of acyclic database schemes. J. Assoc. Comput. Mach. 30 (1983), 479–513.
MR 0709830 |
Zbl 0624.68087
[7] Berge, C.: Discrete Multivariate Analysis. MIT Press, Cambridge 1975.
[8] Csiszár, I.:
I-divergence geometry of probability distributions and minimization problems. Ann. Probab. 3 (1975), 146–158.
MR 0365798
[9] Csiszár, I.:
Maxent, mathematics, and information theory. In: Proc. Internat. Workshop on “Maximum entropy and Bayesian methods", 1995, pp. 35–50.
MR 1446714
[10] Dall’Aglio, G., Kotz, K., Salinetti, G.:
Advances in Probability Distributions with Given Marginals. Kluwer Academic Pub., Dordrecht, Boston, London 1991.
MR 1215942
[11] Darroch, J. N., Ratcliff, D.:
Generalized iterative scaling for log-linear models. Ann. Math. Statist. 43 (1972), 1470–1480.
MR 0345337 |
Zbl 0251.62020
[13] Deming, W. E., Stephan, F. F.:
On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Ann. Math. Statist. 11 (1940), 427–444.
MR 0003527 |
Zbl 0024.05502
[14] Endo, Y., Takemura, A. I.:
Iterative proportional scaling via decomposable submodels for contingency tables. Comput. Statist. Data Analysis 53 (2009), 966–978.
MR 2657062
[15] Fienberg, S. E.:
An iterative procedure for estimation in contingency tables. Ann. Math. Statist. 41 (1970), 907–917.
MR 0266394 |
Zbl 0198.23401
[16] Fienberg, S. E., Meyer, M. M.: Iterative proportional fitting. In: Encyclopedia of Statistical Sciences (S. Kotz, N. L. Johnson, and C. B. Read, eds.), 4, John Wiley and Sons, New York, pp. 275–279.
[17] Haberman, S. J.: Log-linear Models for Contingency Tables. University of Chicago Press, Chicago 1974.
[18] Ireland, C. T., Kullback, S.:
Contingency tables with given marginals. Biometrika 55 (1968), 179–188.
MR 0229329 |
Zbl 0155.26701
[19] Jiroušek, R.: Composition of probability measures on finite spaces. In: Proc. XIII Internat. Conf. Uncertainty in Artificial Intelligence 1997, pp. 274–281.
[20] Jiroušek, R., Přeučil, S.: On the effective implementation of the iterative proportional fitting procedure. Comput. Statist. Data Analysis 19 (1995), 177–189.
[21] Johnson, R. W.:
Axiomatic characterization of the directed divergences and their linear combinations. IEEE Trans. Inform. Theory 25 (1979), 709–716.
MR 0551270 |
Zbl 0422.60016
[22] Kellerer, H. G.:
Verteilungsfunktionen mit gegebenen marginalverteilungen. Zeitschrift Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 247–270.
MR 0175158 |
Zbl 0126.34003
[24] Kern-Isberner, G.:
Characterizing the principle of minimum-cross entropy within a conditional-logical framework. Artificial Intelligence 98 (1998), 169–208.
MR 1614388 |
Zbl 0903.68181
[25] Ku, H. H., Kullback, S.:
Interaction in multidimensional contingency tables: an information-theoretic approach. J. Res. Nat. Bur. Standards - Math. Sci. 72 B (1968), 159–199.
MR 0258223 |
Zbl 0274.62036
[26] Lauritzen, S. L.:
Graphical Models. Oxford Science Pub., Clarendom Press, Oxford 1996.
MR 1419991
[27] Lauritzen, S. L., Speed, M. P., Vijayan, K.:
Decomposable graphs and hypergraphs. J. Austral. Math. Soc. Ser. A 36 (1984), 12–29.
MR 0719998 |
Zbl 0533.05046
[28] Lauritzen, S. L., Spiegelhalter, D. J.:
Local computations with probabilities on graphical structures and their application to expert systems. J. Roy. Stat. Soc. Ser. B 50 (1988), 157–224.
MR 0964177 |
Zbl 0684.68106
[29] Leimer, G.:
Optimal decomposition by clique separators. Discrete Math. 113 (1993), 99–123.
MR 1212872 |
Zbl 0793.05128
[30] Leontief, W. W.: The Structure of American Economy 1919–1929. Oxford University Press, New York 1941.
[31] Leontief, W. W., Strout, A.: Multiregional input-output analysis. In: Structural Interdependence and Economic Development, 1963, pp. 119–169.
[32] Madigan, D., Mosurski, K.:
An extension of the results of Asmussen and Edwards on collapsibility in contingency tables. Biometrika 77 (1990), 315–319.
MR 1064803 |
Zbl 0731.62113
[33] Madigan, D., Mosurski, K.:
Errata: An extension of the results of Asmussen and Edwards on collapsibility in contingency tables. Biometrika 86 (1999) 973.
MR 1741994
[35] Maier, D., Ullman, J. D.:
Connections in acyclic hypergraphs. Theoret. Comput. Sci. 32 (1984), 185–199.
MR 0761167 |
Zbl 0557.05054
[36] Malvestuto, F. M.: Answering queries in categorical data bases. In: Proc. VI ACM Symp. Principles of Database Systems 1987, pp. 87–96.
[37] Malvestuto, F. M.:
Existence of extensions and product extensions for discrete probability distributions. Discrete Math. 69 (1988), 61–77.
MR 0935028 |
Zbl 0637.60021
[38] Malvestuto, F. M.:
Computing the maximum-entropy extension of given discrete probability distributions. Computat. Statist. Data Anal. 8 (1989), 299–311.
MR 1028405 |
Zbl 0726.62012
[39] Malvestuto, F. M.: Testing implication of hierarchical loglinear models for discrete probability distributions. Statist. Computing 6 (1996), 169–176.
[40] Malvestuto, F. M.:
A hypergraph-theoretic analysis of collapsibility and decomposability for extended loglinear models. Statist. Computing 11 (2001), 155–169.
MR 1837135
[41] Malvestuto, F. M.:
From conditional independences to factorization constraints with discrete random variables. Ann. Math. Artificial Intelligence 35 (2002), 253–285.
MR 1899954 |
Zbl 1001.68033
[42] Malvestuto, F. M.:
Canonical and monophonic convexities in hypergraphs. Discrete Math. 309 (2009), 4287–4298.
MR 2519164 |
Zbl 1211.05093
[43] Malvestuto, F. M., Moscarini, M.:
A fast algorithm for query optimization in universal-relation databases. J. Comput. System Sci. 56 (1998), 299–309.
MR 1633981 |
Zbl 0913.68060
[44] Malvestuto, F. M., Moscarini, M.:
Decomposition of a hypergraph by partial-edge separators. Theoret. Comput. Sci. 237 (2000), 57–79.
MR 1756201 |
Zbl 0939.68089
[45] Malvestuto, F. M., Pourabbas, E.: Customized answers to summary queries via aggregate views. In: Proc. XVI Intl. Conf. Scientific & Statistical Database Management 2004, pp. 193–202.
[46] Malvestuto, F. M., Pourabbas, E.: Local computation of answers to table queries on summary databases. In: Proc. XVII Intl. Conf. Scientific & Statistical Database Management 2005, pp. 263–272.
[47] Matúš, F.:
Discrete marginal problem for complex measures. Kybernetika 24 (1988), 36–46.
MR 0936552
[48] Matúš, F.: On the maximum-entropy extensions of probability measures over undirected graphs. In: Proc. III Workshop Uncertainty Processing in Expert Systems 1994, pp. 181–198.
[49] Matúš, F., Flusser, J.: Image representations via a finite Radon transform. IEEE Trans. Pattern Analysis and Machine Intelligence 15 (1993), 996–1006.
[51] Purcell, N. J., Kish, L.:
Postcensal estimates for local areas (or domains). Internat. Statist. Rev. 48 (1980), 3–18.
Zbl 0433.62080
[52] Rüschendorf, L.:
Convergence of the iterative proportional fitting procedure. Ann. Statist. 23 (1995), 1160–1174.
MR 1353500
[53] Shore, J. E., Johnson, R. W.:
Properties of cross-entropy minimization. IEEE Trans. Inform. Theory 27 (1981), 472–482.
MR 0635526 |
Zbl 0459.94008
[54] Stephan, F. F.:
An iterative method of adjusting sample frequencies tables when expected marginal totals are known. Ann. Math. Statist. 13 (1942), 166–178.
MR 0006674
[55]
R. Stone and A. Brown:A Computable Model for Economic Growth: A Programme for Growth, No. 1. Chapman Hall, London 1962.
Zbl 1005.68507
[56] Tarjan, R. E., Yannakakis, M.:
Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce hypergraphs. SIAM J. Comput. 13 (1984), 566–579.
MR 0749707
[57] Vomlel, J.:
Integrating inconsistent data in a probabilistic model. J. Appl. Non-Classical Logics 14 (2004), 365–386.
Zbl 1185.68699
[58] Vorob’ev, N. N.: Consistent families of measures and their extensions. Theor. Prob. Appl. 7 (1962), 147–163.
[59] Vorob’ev, N. N.:
Markov measures and Markov extensions. Theor. Prob. Appl. 8 (1963), 420–429.
MR 0169295
[60] Yannakakis, M.:
Computing the minimum fill-in is NP-complete. SIAM J. Algebraic Discrete Mathematics 2 (1981), 77–79.
MR 0604513 |
Zbl 0496.68033
[61] Yannakakis, M.: Algorithms for acyclic database schemes. In: Proc. VII Internat. Conf. Very Large Data Bases 1981, pp. 82–94.