Sound approximate reasoning about saturated conditional probabilistic independence under controlled uncertainty

Journal of Applied Logic - Tập 11 - Trang 309-327 - 2013
Sebastian Link1
1Department of Computer Science, The University of Auckland, Auckland, New Zealand

Tài liệu tham khảo

Armstrong, 1974, Dependency structures of database relationships, 580 Batista, 2003, An analysis of four missing data treatment methods for supervised learning, Appl. Artif. Intell., 17, 519, 10.1080/713827181 Beeri, 1977, A complete axiomatization for functional and multivalued dependencies in database relations, 47 Beeri, 1984, On the structure of Armstrong relations for functional dependencies, J. ACM, 31, 30, 10.1145/2422.322414 Biskup, 1980, Inferences of multivalued dependencies in fixed and undetermined universes, Theoret. Comput. Sci., 10, 93, 10.1016/0304-3975(80)90075-4 Biskup, 2012, Appropriate inferences of data dependencies in relational databases, Ann. Math. Artif. Intell., 63, 213, 10.1007/s10472-012-9275-0 Biskup, 2012, Probabilistic conditional independence under schema certainty and uncertainty, vol. 7520, 365 Chickering, 1997, Efficient approximations for the marginal likelihood of Bayesian networks with hidden variables, Mach. Learn., 29, 181, 10.1023/A:1007469629108 Ciucci, 2012, Three-valued logics for incomplete information and epistemic logic, vol. 7519, 147 Codd, 1979, Extending the database relational model to capture more meaning, ACM Trans. Database Syst., 4, 397, 10.1145/320107.320109 Codd, 1986, Missing information (applicable and inapplicable) in relational databases, SIGMOD Rec., 15, 53, 10.1145/16301.16303 Darwiche, 1997, A logical notion of conditional independence: Properties and application, Artificial Intelligence, 97, 45, 10.1016/S0004-3702(97)00042-8 Darwiche, 2009 Darwiche, 2010, Bayesian networks, Comm. ACM, 53, 80, 10.1145/1859204.1859227 Dawid, 1979, Conditional independence in statistical theory, J. R. Stat. Soc. Ser. B Stat. Methodol., 41, 1 de Cooman, 2011, Independent natural extension, Artificial Intelligence, 175, 1911, 10.1016/j.artint.2011.06.001 de Waal, 2004, Stable independence and complexity of representation, 112 Dempster, 1977, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B Stat. Methodol., 39, 1 Fagin, 1982, Horn clauses and database dependencies, J. ACM, 29, 952, 10.1145/322344.322347 Fayyad, 1996, From data mining to knowledge discovery in databases, AI Mag., 17, 37 Fienberg, 1972, The analysis of incomplete multi-way contingency tables, Biometrics, 28, 177, 10.2307/2528967 Friedman, 1997, Learning belief networks in presence of missing values and hidden variables, 125 Galil, 1982, An almost linear-time algorithm for computing a dependency basis in a relational database, J. ACM, 29, 96, 10.1145/322290.322296 Geiger, 1990, Logical and algorithmic properties of independence and their application to Bayesian networks, Ann. Math. Artif. Intell., 2, 165, 10.1007/BF01531004 Geiger, 1993, Logical and algorithmic properties of conditional independence and graphical models, Ann. Statist., 21, 2001, 10.1214/aos/1176349407 Grädel, 2013, Dependence and independence, Studia Logica, 101, 399, 10.1007/s11225-013-9479-2 Graetzer, 1998 Halpern, 2005 Hartmann, 2006, On a problem of Fagin concerning multivalued dependencies in relational databases, Theoret. Comput. Sci., 353, 53, 10.1016/j.tcs.2005.08.036 Hartmann, 2012, The implication problem of data dependencies over SQL table definitions: axiomatic, algorithmic and logical characterizations, ACM Trans. Database Syst., 37, 10.1145/2188349.2188355 Hartmann, 2004, Reasoning about functional and multi-valued dependencies in the presence of lists, vol. 2942, 134 Hartmann, 2011, On Codd families of keys over incomplete relations, Comput. J., 54, 1166, 10.1093/comjnl/bxq073 Hartmann, 2012, Design by example for SQL table definitions with functional dependencies, VLDB J., 21, 121, 10.1007/s00778-011-0239-5 Herrmann, 1995, On the undecidability of implications between embedded multivalued database dependencies, Inform. and Comput., 122, 221, 10.1006/inco.1995.1148 Herrmann, 2006, Corrigendum to “On the undecidability of implications between embedded multivalued database dependencies”, Inform. and Comput., 204, 1847, 10.1016/j.ic.2006.09.002 Ivanovska, 2010, Probabilistic logic with conditional independence formulae, 983 Lang, 2002, Conditional independence in propositional logic, Artificial Intelligence, 141, 79, 10.1016/S0004-3702(02)00244-8 Langeveldt, 2010, Empirical evidence for the usefulness of Armstrong relations on the acquisition of meaningful functional dependencies, Inf. Syst., 35, 352, 10.1016/j.is.2009.11.002 Lauritzen, 1995, The EM algorithm for graphical association models with missing data, Comput. Stat. Data Anal., 19, 191, 10.1016/0167-9473(93)E0056-A Levene, 1998, Axiomatisation of functional dependencies in incomplete relations, Theoret. Comput. Sci., 206, 283, 10.1016/S0304-3975(98)80029-7 Levesque, 1989, A knowledge-level account of abduction, 1061 Link, 2008, Charting the completeness frontier of inference systems for multivalued dependencies, Acta Inform., 45, 565, 10.1007/s00236-008-0080-5 Link, 2008, On the implication of multivalued dependencies in partial database relations, Internat. J. Found. Comput. Sci., 19, 691, 10.1142/S0129054108005899 Link, 2012, Characterizations of multivalued dependency implication over undetermined universes, J. Comput. System Sci., 78, 1026, 10.1016/j.jcss.2011.12.012 Link, 2012, Propositional reasoning about saturated conditional probabilistic independence, vol. 7456, 257 Lou, 2012, Margin-based feature selection in incomplete data, 1040 Malvestuto, 1992, A unique formal system for binary decompositions of database relations, probability distributions, and graphs, Inform. Sci., 59, 21, 10.1016/0020-0255(92)90042-7 Mannila, 1986, Design by example: An application of Armstrong relations, J. Comput. System Sci., 33, 126, 10.1016/0022-0000(86)90015-2 Marlin, 2011, Recommender systems, missing data and statistical model estimation, 2686 Matúš, 1992, Ascending and descending conditional independence relations, 189 More, 2010, An independence relation for sets of secrets, Studia Logica, 94, 73, 10.1007/s11225-010-9223-0 Naumov, 2012, Independence in information spaces, Studia Logica, 100, 953, 10.1007/s11225-012-9435-6 Niepert, 2008, On the conditional independence implication problem: A lattice-theoretic approach, 435 Niepert, 2010, Logical and algorithmic properties of stable conditional independence, Internat. J. Approx. Reason., 51, 531, 10.1016/j.ijar.2010.01.011 Pearl, 1988 Saar-Tsechansky, 2007, Handling missing values when applying classification models, J. Mach. Learn. Res., 8, 1623 Sagiv, 1980, An algorithm for inferring multivalued dependencies with an application to propositional logic, J. ACM, 27, 250, 10.1145/322186.322190 Sagiv, 1981, An equivalence between relational database dependencies and a fragment of propositional logic, J. ACM, 28, 435, 10.1145/322261.322263 Schaerf, 1995, Tractable reasoning via approximation, Artificial Intelligence, 74, 249, 10.1016/0004-3702(94)00009-P Singh, 1997, Learning Bayesian networks from incomplete data, 534 Stefanini, 2013, Graphical models for eliciting structural information, 139 Stott Parker, 1980, Inferences involving embedded multivalued dependencies and transitive dependencies, 52 Studený, 1992, Conditional independence relations have no finite complete characterization, 377 Studený, 2005 Wong, 2000, On the implication problem for probabilistic conditional independency, IEEE Trans. Syst. Man Cybern., Part A, Syst. Humans, 30, 785, 10.1109/3468.895901 Zaniolo, 1984, Database relations with null values, J. Comput. System Sci., 28, 142, 10.1016/0022-0000(84)90080-1 Zhang, 2011, Missing data imputation by utilizing information within incomplete instances, J. Syst. Softw., 84, 452, 10.1016/j.jss.2010.11.887 Zhu, 2007, Cost-sensitive imputing missing values with ordering, 1922