Probabilistic databases

Many applications today need to manage large data sets with uncertainties. In this paper we describe the foundations of managing data where the uncertainties are quantified as probabilities. We review the basic definitions of the probabilistic data model and present some fundamental theoretical results for query evaluation on probabilistic databases.

[1]  H. V. Jagadish,et al.  ProTDB: Probabilistic Data in XML , 2002, VLDB.

[2]  Daisy Zhe Wang,et al.  Querying probabilistic information extraction , 2010, Proc. VLDB Endow..

[3]  R. Snodgrass The temporal query language TQuel , 1984, ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems.

[4]  V. S. Subrahmanian,et al.  Aggregate Query Answering under Uncertain Schema Mappings , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[5]  Georg Gottlob,et al.  Hypertree decompositions and tractable queries , 1998, J. Comput. Syst. Sci..

[6]  Shai Ben-David,et al.  ProbClean: A probabilistic duplicate detection system , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[7]  Sunil Prabhakar,et al.  Evaluating probabilistic queries over imprecise data , 2003, SIGMOD '03.

[8]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[9]  Alexander S. Szalay,et al.  Data Management in the Worldwide Sensor Web , 2007, IEEE Pervasive Computing.

[10]  Christoph Koch,et al.  Approximating predicates and expressive queries on probabilistic databases , 2008, PODS.

[11]  Dan Suciu,et al.  An overview of semistructured data , 1998, SIGA.

[12]  Robert J. McEliece,et al.  The generalized distributive law , 2000, IEEE Trans. Inf. Theory.

[13]  Jennifer Widom,et al.  Representing uncertain data: models, properties, and algorithms , 2009, The VLDB Journal.

[14]  Jianzhong Li,et al.  Finding top-k maximal cliques in an uncertain graph , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[15]  Andrew McCallum,et al.  Scalable probabilistic databases with factor graphs and MCMC , 2010, Proc. VLDB Endow..

[16]  Jennifer Widom,et al.  An Introduction to ULDBs and the Trio System , 2006, IEEE Data Eng. Bull..

[17]  Lise Getoor,et al.  Read-once functions and query evaluation in probabilistic databases , 2010, Proc. VLDB Endow..

[18]  Jacob Köhler,et al.  Addressing the problems with life-science databases for traditional uses and systems biology , 2006, Nature Reviews Genetics.

[19]  Dan Olteanu,et al.  Using OBDDs for Efficient Query Evaluation on Probabilistic Databases , 2008, SUM.

[20]  Laks V. S. Lakshmanan,et al.  ProbView: a flexible probabilistic database system , 1997, TODS.

[21]  Raghu Ramakrishnan,et al.  DBLife: A Community Information Management Platform for the Database Research Community (Demo) , 2007, CIDR.

[22]  Susanne E. Hambrusch,et al.  Indexing Uncertain Categorical Data , 2007, 2007 IEEE 23rd International Conference on Data Engineering.

[23]  Dan Olteanu,et al.  Approximate confidence computation in probabilistic databases , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[24]  Kevin Chen-Chuan Chang,et al.  Probabilistic top-k and ranking-aggregate queries , 2008, TODS.

[25]  Daisy Zhe Wang,et al.  BayesStore: managing large, uncertain data repositories with probabilistic graphical models , 2008, Proc. VLDB Endow..

[26]  Adnan Darwiche,et al.  A differential approach to inference in Bayesian networks , 2000, JACM.

[27]  Feifei Li,et al.  Ranking distributed probabilistic data , 2009, SIGMOD Conference.

[28]  Yehoshua Sagiv,et al.  Query evaluation over probabilistic XML , 2009, The VLDB Journal.

[29]  Luca Trevisan A Note on Deterministic Approximate Counting for k-DNF , 2002, Electron. Colloquium Comput. Complex..

[30]  Dan Olteanu,et al.  $${10^{(10^{6})}}$$ worlds and beyond: efficient representation and processing of incomplete information , 2006, 2007 IEEE 23rd International Conference on Data Engineering.

[31]  Eugene Wong,et al.  A statistical approach to incomplete information in database systems , 1982, TODS.

[32]  Christopher Ré,et al.  The trichotomy of HAVING queries on a probabilistic database , 2009, The VLDB Journal.

[33]  Christopher Ré,et al.  Approximation trade-offs in Markovian stream processing: An empirical study , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[34]  S. Madden,et al.  UPI: A Primary Index for Uncertain Databases , 2010, Proc. VLDB Endow..

[35]  Kousha Etessami,et al.  Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations , 2005, JACM.

[36]  Wei Hong,et al.  Model-Driven Data Acquisition in Sensor Networks , 2004, VLDB.

[37]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[38]  Jian Zhou,et al.  Off-Line Handwritten Word Recognition Using a Hidden Markov Model Type Stochastic Network , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[39]  Dan Olteanu,et al.  MayBMS: a probabilistic database management system , 2009, SIGMOD Conference.

[40]  Feifei Li,et al.  Probabilistic string similarity joins , 2010, SIGMOD Conference.

[41]  Dan Suciu,et al.  Towards correcting input data errors probabilistically using integrity constraints , 2006, MobiDE '06.

[42]  Samuel Madden,et al.  Using Probabilistic Models for Data Management in Acquisitional Environments , 2005, CIDR.

[43]  David Poole,et al.  First-order probabilistic inference , 2003, IJCAI.

[44]  Prithviraj Sen,et al.  Representing and Querying Correlated Tuples in Probabilistic Databases , 2007, 2007 IEEE 23rd International Conference on Data Engineering.

[45]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[46]  Phokion G. Kolaitis,et al.  Probabilistic data exchange , 2011, ICDT '10.

[47]  Christopher Ré,et al.  Query Evaluation on Probabilistic Databases , 2006, IEEE Data Eng. Bull..

[48]  Xi Zhang,et al.  On the semantics and evaluation of top-k queries in probabilistic databases , 2008, ICDE Workshops.

[49]  Phokion G. Kolaitis,et al.  Subtractive Reductions and Complete Problems for Counting Complexity Classes , 2000, MFCS.

[50]  Serge Abiteboul,et al.  On the representation and querying of sets of possible worlds , 1987, SIGMOD '87.

[51]  Christopher Ré,et al.  Materialized Views in Probabilistic Databases for Information Exchange and Query Optimization , 2007, VLDB.

[52]  Hans-Jörg Schek,et al.  The relational model with relation-valued attributes , 1986, Inf. Syst..

[53]  Renée J. Miller,et al.  Creating probabilistic databases from duplicated data , 2009, The VLDB Journal.

[54]  W. Clem Karl,et al.  Multiscale segmentation and anomaly enhancement of SAR imagery , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[55]  Jeffrey Xu Yu,et al.  Probabilistic Skyline Operator over Sliding Windows , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[56]  Dan Olteanu,et al.  Secondary-storage confidence computation for conjunctive queries with inequalities , 2009, SIGMOD Conference.

[57]  Prashant J. Shenoy,et al.  Probabilistic Inference over RFID Streams in Mobile Environments , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[58]  Sunil Prabhakar,et al.  Managing uncertainty in sensor database , 2003, SGMD.

[59]  Gösta Grahne,et al.  Dependency Satisfaction in Databases with Incomplete Information , 1984, VLDB.

[60]  Adnan Darwiche Searching While Keeping a Trace: The Evolution from Satisfiability to Knowledge Compilation , 2006, IJCAR.

[61]  Christopher Ré,et al.  Efficient Evaluation of , 2007, DBPL.

[62]  Jeffrey D. Ullman,et al.  Principles of Database and Knowledge-Base Systems, Volume II , 1988, Principles of computer science series.

[63]  Michael I. Jordan Learning in Graphical Models , 1999, NATO ASI Series.

[64]  Tomasz Imielinski,et al.  Incomplete Information in Relational Databases , 1984, JACM.

[65]  Susanne E. Hambrusch,et al.  Orion 2.0: native support for uncertain data , 2008, SIGMOD Conference.

[66]  Constance de Koning,et al.  Editors , 2003, Annals of Emergency Medicine.

[67]  Dan Suciu,et al.  Access control over uncertain data , 2008, Proc. VLDB Endow..

[68]  Lise Getoor,et al.  Learning Probabilistic Relational Models , 1999, IJCAI.

[69]  Michel de Rougemont,et al.  The Reliability of Queries. , 1995, ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems.

[70]  Dan Olteanu,et al.  10106 Worlds and Beyond: Efficient Representation and Processing of Incomplete Information , 2007, ICDE.

[71]  L. Libkin,et al.  Semantic representations and query languages for or-sets , 1993, J. Comput. Syst. Sci..

[72]  Val Tannen,et al.  Provenance semirings , 2007, PODS.

[73]  Daniel Deutch,et al.  On models and query languages for probabilistic processes , 2010, SGMD.

[74]  Lawrence K. Saul,et al.  Large Margin Hidden Markov Models for Automatic Speech Recognition , 2006, NIPS.

[75]  Christoph Koch,et al.  On Query Algebras for Probabilistic Databases , 2009, SGMD.

[76]  Gautam Das,et al.  Leveraging COUNT Information in Sampling Hidden Databases , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[77]  Yehoshua Sagiv,et al.  Query efficiency in probabilistic XML models , 2008, SIGMOD Conference.

[78]  Joann J. Ordille,et al.  Data integration: the teenage years , 2006, VLDB.

[79]  Helen J. Wang,et al.  Online aggregation , 1997, SIGMOD '97.

[80]  Dan Suciu,et al.  Management of probabilistic data: foundations and challenges , 2007, PODS '07.

[81]  Ezio Lefons,et al.  An Analytic Approach to Statistical Databases , 1983, VLDB.

[82]  Feifei Li,et al.  Semantics of Ranking Queries for Probabilistic Data and Expected Ranks , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[83]  Michel de Rougemont The reliability of queries (extended abstract) , 1995, PODS '95.

[84]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[85]  Jennifer Widom,et al.  Exploiting Lineage for Confidence Computation in Uncertain and Probabilistic Databases , 2008, 2008 IEEE 24th International Conference on Data Engineering.

[86]  Ingo Wegener,et al.  BDDs--design, analysis, complexity, and applications , 2004, Discret. Appl. Math..

[87]  Stanley B. Zdonik,et al.  Top-k queries on uncertain data: on score distribution and typical answers , 2009, SIGMOD Conference.

[88]  Dan Suciu,et al.  Integrating and Ranking Uncertain Scientific Data , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[89]  Amol Deshpande,et al.  Lineage processing over correlated probabilistic databases , 2010, SIGMOD Conference.

[90]  George Kollios,et al.  k-nearest neighbors in uncertain graphs , 2010, Proc. VLDB Endow..

[91]  Amol Deshpande,et al.  Indexing correlated probabilistic databases , 2009, SIGMOD Conference.

[92]  Ihab F. Ilyas,et al.  Supporting ranking queries on uncertain and incomplete data , 2010, The VLDB Journal.

[93]  Takashi Saito,et al.  Semantics analysis through elementary meanings: theoretical foundation for generalized thesaurus construction , 2000 .

[94]  Cassio P. de Campos Tutorial: Graphical Models , 2009 .

[95]  Christopher Ré,et al.  Efficient Top-k Query Evaluation on Probabilistic Data , 2007, 2007 IEEE 23rd International Conference on Data Engineering.

[96]  Dan Suciu,et al.  The Boundary Between Privacy and Utility in Data Publishing , 2007, VLDB.

[97]  E. F. Codd,et al.  Relational Completeness of Data Base Sublanguages , 1972, Research Report / RJ / IBM / San Jose, California.

[98]  Christoph Koch,et al.  PIP: A database system for great and small expectations , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[99]  Christopher Ré,et al.  Approximate lineage for probabilistic databases , 2008, Proc. VLDB Endow..

[100]  Anthony J. Bonner,et al.  Querying sequence databases with transducers , 2000, Acta Informatica.

[101]  Michael Luby,et al.  Approximating Probabilistic Inference in Bayesian Belief Networks is NP-Hard , 1993, Artif. Intell..

[102]  Serge Abiteboul,et al.  Querying and Updating Probabilistic Information in XML , 2006, EDBT.

[103]  Blake Hannaford,et al.  A Hybrid Discriminative/Generative Approach for Modeling Human Activities , 2005, IJCAI.

[104]  Christopher Ré,et al.  Managing Uncertainty in Social Networks , 2007, IEEE Data Eng. Bull..

[105]  Ben Taskar,et al.  Selectivity estimation using probabilistic models , 2001, SIGMOD '01.

[106]  Graham Cormode,et al.  Histograms and Wavelets on Probabilistic Data , 2008, IEEE Transactions on Knowledge and Data Engineering.

[107]  Dan Suciu,et al.  Bridging the gap between intensional and extensional query evaluation in probabilistic databases , 2010, EDBT '10.

[108]  Leonid Libkin,et al.  Elements of Finite Model Theory , 2004, Texts in Theoretical Computer Science.

[109]  Richard M. Karp,et al.  Monte-Carlo Approximation Algorithms for Enumeration Problems , 1989, J. Algorithms.

[110]  J. Scott Provan,et al.  The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected , 1983, SIAM J. Comput..

[111]  Fernando Pereira,et al.  Shallow Parsing with Conditional Random Fields , 2003, NAACL.

[112]  Hui Jiang,et al.  Large margin hidden Markov models for speech recognition , 2006, IEEE Transactions on Audio, Speech, and Language Processing.

[113]  Jennifer Widom,et al.  Trio: A System for Integrated Management of Data, Accuracy, and Lineage , 2004, CIDR.

[114]  Sakti P. Ghosh Statistical relational tables for statistical database management , 1986, IEEE Transactions on Software Engineering.

[115]  Esteban Zimányi,et al.  Query Evaluation in Probabilistic Relational Databases , 1997, Theor. Comput. Sci..

[116]  Michael Pittarelli,et al.  The Theory of Probabilistic Databases , 1987, VLDB.

[117]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[118]  Sunil Prabhakar,et al.  Threshold query optimization for uncertain data , 2010, SIGMOD Conference.

[119]  Rahul Gupta,et al.  Creating probabilistic databases from information extraction models , 2006, VLDB.

[120]  Dan Roth,et al.  On the Hardness of Approximate Reasoning , 1993, IJCAI.

[121]  Bertram Ludäscher,et al.  A Transducer-Based XML Query Processor , 2002, VLDB.

[122]  Dan Olteanu,et al.  SPROUT: Lazy vs. Eager Query Plans for Tuple-Independent Probabilistic Databases , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[123]  Stéphane Grumbach,et al.  Constraint Databases , 1999, JFPLC.

[124]  Parag Agrawal,et al.  Towards Special-Purpose Indexes and Statistics for Uncertain Data , 2008, QDB/MUD.

[125]  Serge Abiteboul,et al.  On the complexity of managing probabilistic XML data , 2007, PODS '07.

[126]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[127]  Jennifer Widom,et al.  Working Models for Uncertain Data , 2006, 22nd International Conference on Data Engineering (ICDE'06).

[128]  Jennifer Widom,et al.  Schema Design for Uncertain Databases , 2007, AMW.

[129]  Doug Downey,et al.  Web-scale information extraction in knowitall: (preliminary results) , 2004, WWW '04.

[130]  Renée J. Miller,et al.  Clean Answers over Dirty Databases: A Probabilistic Approach , 2006, 22nd International Conference on Data Engineering (ICDE'06).

[131]  Norbert Fuhr,et al.  A probabilistic relational algebra for the integration of information retrieval and database systems , 1997, TOIS.

[132]  Peter J. Haas,et al.  E = MC3: managing uncertain enterprise data in a cluster-computing environment , 2009, SIGMOD Conference.

[133]  Geoffrey S. F. Ling,et al.  Invited talk , 2007 .

[134]  Alon Y. Halevy,et al.  Answering queries using views: A survey , 2001, The VLDB Journal.

[135]  Maurice van Keulen,et al.  A probabilistic XML approach to data integration , 2005, 21st International Conference on Data Engineering (ICDE'05).

[136]  Dan Suciu,et al.  Computing query probability with incidence algebras , 2010, PODS '10.

[137]  Sriram Raghavan,et al.  Avatar Information Extraction System , 2006, IEEE Data Eng. Bull..

[138]  Raghu Ramakrishnan,et al.  Community Information Management , 2006, IEEE Data Eng. Bull..

[139]  Frank Neven,et al.  Typechecking Top-Down Uniform Unranked Tree Transducers , 2003, ICDT.

[140]  Anthony J. Bonner,et al.  Sequences, Datalog, and Transducers , 1998, J. Comput. Syst. Sci..

[141]  Christopher Ré,et al.  Implementing NOT EXISTS Predicates over a Probabilistic Database , 2008, QDB/MUD.

[142]  Saul A. Kripke,et al.  Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[143]  Nilesh N. Dalvi,et al.  Robust web extraction: an approach based on a probabilistic tree-edit model , 2009, SIGMOD Conference.

[144]  Hector Garcia-Molina,et al.  The Management of Probabilistic Data , 1992, IEEE Trans. Knowl. Data Eng..

[145]  Salil P. Vadhan,et al.  Computational Complexity , 2005, Encyclopedia of Cryptography and Security.

[146]  Jennifer Widom,et al.  Databases with uncertainty and lineage , 2008, The VLDB Journal.

[147]  Joseph Y. Halpern,et al.  From Statistical Knowledge Bases to Degrees of Belief , 1996, Artif. Intell..

[148]  Daniel Deutch,et al.  On probabilistic fixpoint and Markov chain query languages , 2010, PODS '10.

[149]  E. F. Codd,et al.  A relational model of data for large shared data banks , 1970, CACM.

[150]  Dan Olteanu,et al.  MayBMS: Managing Incomplete Information with Probabilistic World-Set Decompositions , 2007, 2007 IEEE 23rd International Conference on Data Engineering.

[151]  Dan Suciu,et al.  A formal analysis of information disclosure in data exchange , 2004, SIGMOD '04.

[152]  Xike Xie,et al.  UV-diagram: A Voronoi diagram for uncertain data , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[153]  Sumit Sarkar,et al.  A probabilistic relational model and algebra , 1996, TODS.

[154]  Reynold Cheng,et al.  Managing uncertainty of XML schema matching , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[155]  Sean R. Collins,et al.  Global landscape of protein complexes in the yeast Saccharomyces cerevisiae , 2006, Nature.

[156]  Adnan Darwiche,et al.  Decomposable negation normal form , 2001, JACM.

[157]  J. Hintikka Semantics for Propositional Attitudes , 1969 .

[158]  David J. Spiegelhalter,et al.  Probabilistic Networks and Expert Systems , 1999, Information Science and Statistics.

[159]  Mikhail J. Atallah,et al.  Computing all skyline probabilities for uncertain data , 2009, PODS.

[160]  Jennifer Widom,et al.  ULDBs: databases with uncertainty and lineage , 2006, VLDB.

[161]  E. F. Codd,et al.  A Relational Model for Large Shared Data Banks , 1970 .

[162]  Luca Trevisan,et al.  A Note on Approximate Counting for k-DNF , 2004, APPROX-RANDOM.

[163]  Matthai Philipose,et al.  Towards Activity Databases: Using Sensors and Statistical Models to Summarize People's Lives , 2006, IEEE Data Eng. Bull..

[164]  Christoph E. Koch MayBMS: A System for Managing Large Uncertain and Probabilistic Databases , 2009 .

[165]  Adnan Darwiche Relax, Compensate and Then Recover: A Theory of Anytime, Approximate Inference , 2010, JELIA.

[166]  Nevin Lianwen Zhang,et al.  Exploiting Contextual Independence In Probabilistic Inference , 2011, J. Artif. Intell. Res..

[167]  Dan Suciu,et al.  Efficient query evaluation on probabilistic databases , 2004, The VLDB Journal.

[168]  Peter J. Haas,et al.  Resolution-Aware Query Answering for Business Intelligence , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[169]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[170]  Dan Olteanu,et al.  Fast and Simple Relational Processing of Uncertain Data , 2007, 2008 IEEE 24th International Conference on Data Engineering.

[171]  Ernest W. Adams,et al.  A primer of probability logic , 1996 .

[172]  Gösta Grahne,et al.  The Problem of Incomplete Information in Relational Databases , 1991, Lecture Notes in Computer Science.

[173]  Yuri Gurevich,et al.  The complexity of query reliability , 1998, PODS.

[174]  Dan Olteanu,et al.  Conditioning probabilistic databases , 2008, Proc. VLDB Endow..

[175]  Charalambos A. Charalambides,et al.  Enumerative combinatorics , 2018, SIGA.

[176]  Jörg Flum,et al.  Query evaluation via tree-decompositions , 2001, JACM.

[177]  Val Tannen,et al.  Models for Incomplete and Probabilistic Information , 2006, IEEE Data Eng. Bull..

[178]  Daisy Zhe Wang,et al.  Declarative Information Extraction in a Probabilistic Database System , 2009 .

[179]  Peter J. Haas,et al.  MCDB: a monte carlo approach to managing uncertain data , 2008, SIGMOD Conference.

[180]  Erol Gelenbe,et al.  A probability model of uncertainty in data bases , 1986, 1986 IEEE Second International Conference on Data Engineering.

[181]  Lise Getoor,et al.  Exploiting shared correlations in probabilistic databases , 2008, Proc. VLDB Endow..

[182]  Maurice van Keulen,et al.  Qualitative effects of knowledge rules and user feedback in probabilistic data integration , 2009, The VLDB Journal.

[183]  O. Deux,et al.  The story of O 2 , 1992 .

[184]  Moni Naor,et al.  Optimal aggregation algorithms for middleware , 2001, PODS.

[185]  Richard M. Karp,et al.  Monte-Carlo algorithms for enumeration and reliability problems , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[186]  Dan Olteanu,et al.  From complete to incomplete information and back , 2007, SIGMOD '07.

[187]  Dan Suciu,et al.  Probabilistic Event Extraction from RFID Data , 2008, 2008 IEEE 24th International Conference on Data Engineering.

[188]  O. Deux,et al.  The Story of O2 , 1990, IEEE Trans. Knowl. Data Eng..

[189]  Subbarao Kambhampati,et al.  Query processing over incomplete autonomous databases: query rewriting using learned data dependencies , 2009, The VLDB Journal.

[190]  Alon Y. Halevy,et al.  Data integration with uncertainty , 2007, The VLDB Journal.

[191]  Udi Rotics,et al.  Read-Once Functions Revisited and the Readability Number of a Boolean Function , 2005, Electron. Notes Discret. Math..

[192]  Jian Li,et al.  Consensus answers for queries over probabilistic databases , 2008, PODS.

[193]  David Poole,et al.  Probabilistic Horn Abduction and Bayesian Networks , 1993, Artif. Intell..

[194]  Richard M. Karp,et al.  An optimal algorithm for Monte Carlo estimation , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[195]  Feifei Li,et al.  Finding frequent items in probabilistic data , 2008, SIGMOD Conference.

[196]  Judea Pearl,et al.  Causal networks: semantics and expressiveness , 2013, UAI.

[197]  Yufei Tao,et al.  Indexing uncertain data , 2009, PODS.

[198]  Dan Suciu,et al.  The dichotomy of conjunctive queries on probabilistic structures , 2006, PODS.

[199]  Gregory F. Cooper,et al.  The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks , 1990, Artif. Intell..

[200]  Leslie G. Valiant,et al.  The Complexity of Enumeration and Reliability Problems , 1979, SIAM J. Comput..

[201]  Moshe Y. Vardi The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[202]  Lise Getoor,et al.  PrDB: managing and exploiting rich correlations in probabilistic databases , 2009, The VLDB Journal.

[203]  Amol Deshpande,et al.  Online Filtering, Smoothing and Probabilistic Modeling of Streaming data , 2008, 2008 IEEE 24th International Conference on Data Engineering.

[204]  Christopher Ré,et al.  Access Methods for Markovian Streams , 2009, 2009 IEEE 25th International Conference on Data Engineering.

[205]  Andrew McCallum,et al.  Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data , 2001, ICML.

[206]  Christoph Koch,et al.  A compositional framework for complex queries over uncertain data , 2009, ICDT '09.

[207]  Daisy Zhe Wang,et al.  Probabilistic declarative information extraction , 2010, 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010).

[208]  Christopher Ré,et al.  Event queries on correlated probabilistic streams , 2008, SIGMOD Conference.

[209]  Yehoshua Sagiv,et al.  Running tree automata on probabilistic XML , 2009, PODS.

[210]  Parag Agrawal,et al.  Trio: a system for data, uncertainty, and lineage , 2006, VLDB.

[211]  Anastasia Ailamaki,et al.  Challenges inbuilding a DBMS Resource Advisor , 2006, IEEE Data Eng. Bull..

[212]  Patrick Valduriez,et al.  Join indices , 1987, TODS.

[213]  V. S. Subrahmanian,et al.  PXML: a probabilistic semistructured data model and algebra , 2003, Proceedings 19th International Conference on Data Engineering (Cat. No.03CH37405).

[214]  Christoph Koch,et al.  World-set decompositions: Expressiveness and efficient algorithms , 2007, Theor. Comput. Sci..