The Veracity of Big Data
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- Erica Osborne
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1 The Veracity of Big Data Pierre Senellart École normale supérieure 13 October 2016, Big Data & Market Insights
2 23 April 2013, Dow Jones (cnn.com)
3 23 April 2013, Dow Jones (cnn.com)
4 23 April 2013, Dow Jones (cnn.com) Twitter feed of Associated Press hacked Algorithmic trading systems reacting to tweets
5 The Four Vs of Big Data 3 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
6 The Four Vs of Big Data Volume: Data volumes beyond what is manageable by traditional data management systems (from TB to PB to EB) 3 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
7 The Four Vs of Big Data Volume: Data volumes beyond what is manageable by traditional data management systems (from TB to PB to EB) Variety: Very diverse forms of data (text, multimedia, graphs, structured data), very diverse organization of data 3 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
8 The Four Vs of Big Data Volume: Data volumes beyond what is manageable by traditional data management systems (from TB to PB to EB) Variety: Very diverse forms of data (text, multimedia, graphs, structured data), very diverse organization of data Velocity: Data produced or changing at high speed (LHC: 100,000,000 collisions / second), more than able to store 3 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
9 The Four Vs of Big Data Volume: Data volumes beyond what is manageable by traditional data management systems (from TB to PB to EB) Variety: Very diverse forms of data (text, multimedia, graphs, structured data), very diverse organization of data Velocity: Data produced or changing at high speed (LHC: 100,000,000 collisions / second), more than able to store Veracity: Data quality very diverse; imprecise, imperfect, untrustworthy information 3 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
10 Uncertain data is everywhere Numerous sources of uncertain data: Measurement errors Data integration from contradicting sources Imprecise mappings between heterogeneous schemas Imprecise automatic processes (information extraction, classification, natural language processing, etc.) Imperfect human judgment Lies, opinions, rumors 4 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
11 Uncertain data is everywhere Numerous sources of uncertain data: Measurement errors Data integration from contradicting sources Imprecise mappings between heterogeneous schemas Imprecise automatic processes (information extraction, classification, natural language processing, etc.) Imperfect human judgment Lies, opinions, rumors 4 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
12 Uncertainty in Web information extraction Never-ending Language Learning (NELL, CMU), 5 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
13 Uncertainty in Web information extraction Google Squared (terminated), screenshot from (Fink et al. 2011) 5 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
14 Uncertainty in Web information extraction Subject Predicate Object Confidence Elvis Presley diedondate % Elvis Presley ismarriedto Priscilla Presley 97.29% Elvis Presley influences Carlo Wolff 96.25% YAGO, (Suchanek et al. 2007) 5 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
15 Dealing with Uncertainty Three main research questions: How to estimate the veracity of a source, or of a piece of information? ) truth finding 6 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
16 Dealing with Uncertainty Three main research questions: How to estimate the veracity of a source, or of a piece of information? ) truth finding How to ensure the provenance of a piece of information, to know where it comes from? ) provenance management 6 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
17 Dealing with Uncertainty Three main research questions: How to estimate the veracity of a source, or of a piece of information? ) truth finding How to ensure the provenance of a piece of information, to know where it comes from? ) provenance management How to efficiently process uncertain data at scale? ) probabilistic database management systems 6 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
18 Outline Introduction Truth Finding Setting Model Experiments Probabilistic Databases Conclusion 7 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
19 Outline Introduction Truth Finding Setting Model Experiments Probabilistic Databases Conclusion 8 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
20 Motivating Example What are the capital cities of European countries? France Italy Poland Romania Hungary Alice Paris Rome Warsaw Bucharest Budapest Bob? Rome Warsaw Bucharest Budapest Charlie Paris Rome Katowice Bucharest Budapest David Paris Rome Bratislava Budapest Sofia Eve Paris Florence Warsaw Budapest Sofia Fred Rome?? Budapest Sofia George Rome??? Sofia 9 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
21 Voting Information: redundance France Italy Poland Romania Hungary Alice Paris Rome Warsaw Bucharest Budapest Bob? Rome Warsaw Bucharest Budapest Charlie Paris Rome Katowice Bucharest Budapest David Paris Rome Bratislava Budapest Sofia Eve Paris Florence Warsaw Budapest Sofia Fred Rome?? Budapest Sofia George Rome??? Sofia Frequence P R W Buch Bud R F K Bud S B / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
22 Evaluating Trustworthiness of Sources Information: redundance, trustworthiness of sources (= average frequence of predicted correctness) France Italy Poland Romania Hungary Trust Alice Paris Rome Warsaw Bucharest Budapest 0.60 Bob? Rome Warsaw Bucharest Budapest 0.58 Charlie Paris Rome Katowice Bucharest Budapest 0.52 David Paris Rome Bratislava Budapest Sofia 0.55 Eve Paris Florence Warsaw Budapest Sofia 0.51 Fred Rome?? Budapest Sofia 0.47 George Rome??? Sofia 0.45 Frequence P R W Buch Bud weighted R F K Bud S by trust B / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
23 Iterative Fixpoint Computation Information: redundance, trustworthiness of sources with iterative fixpoint computation France Italy Poland Romania Hungary Trust Alice Paris Rome Warsaw Bucharest Budapest 0.65 Bob? Rome Warsaw Bucharest Budapest 0.63 Charlie Paris Rome Katowice Bucharest Budapest 0.57 David Paris Rome Bratislava Budapest Sofia 0.54 Eve Paris Florence Warsaw Budapest Sofia 0.49 Fred Rome?? Budapest Sofia 0.39 George Rome??? Sofia 0.37 Frequence P R W Buch Bud weighted R F K Bud S by trust B / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
24 Context and problem Context: Set of sources stating facts (Possible) functional dependencies between facts Fully unsupervised setting: we do not assume any information on truth values of facts or inherent trust in sources Problem: determine which facts are true and which facts are false Real world applications: query answering, source selection, data quality assessment on the web, making good use of the wisdom of crowds 13 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
25 Outline Introduction Truth Finding Setting Model Experiments Probabilistic Databases Conclusion 14 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
26 General Model Set of facts F = ff 1 :::f n g Examples: Paris is capital of France, Rome is capital of France, Rome is capital of Italy Set of views (= sources) V = fv 1 :::V m g, where a view is a partial mapping from F to {T, F} Example: : Paris is capital of France ^ Rome is capital of France Objective: find the most likely real world W given V where the real world is a total mapping from F to {T, F} Example: Paris is capital of France ^ : Rome is capital of France ^ Rome is capital of Italy ^ / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
27 Generative Probabilistic Model (Galland et al. 2010)? V i, f j '(V i )'(f j ) 1 '(V i )'(f j ) "(V i )"(f j ) 1 "(V i )"(f j ) :W(f j ) W(f j ) '(V i )'(f j ): probability that V i forgets f j "(V i )"(f j ): probability that V i makes an error on f j Number of parameters: n + 2(n + m) Size of data: ~'nm with ~' the average forget rate 16 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
28 Obvious Approach Method: use this generative model to find the most likely parameters given the data Inverse the generative model to compute the probability of a set of parameters given the data Not practically applicable: Non-linearity of the model and boolean parameter W (f j ) ) equations for inversing the generative model very complex Large number of parameters (n and m can both be quite large) ) Any exponential technique unpractical ) Heuristic fix-point algorithms (many proposed ones!) 17 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
29 Outline Introduction Truth Finding Setting Model Experiments Probabilistic Databases Conclusion 18 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
30 Hubdub (1/2) questions, 1 to 20 answers, 473 participants 19 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
31 Hubdub (2/2) Number of errors (no post-filtering) Number of errors (with post-filtering) Voting Counting TruthFinder (Yin et al. 2007) 3-Estimates (Galland et al. 2010) 20 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
32 General-Knowledge Quiz (1/2) 17 questions, 4 to 14 answers, 601 participants 21 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
33 General-Knowledge Quiz (2/2) Number of errors (no post-filtering) Number of errors (with post-filtering) Voting 11 6 Counting 12 6 TruthFinder (Yin et al. 2007) 3-Estimates 9 0 (Galland et al. 2010) 22 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
34 Many variations... Modeling of various real-world phenomena: Sources copying each other (Dong et al. 2010) Complex source dependencies (Pochampally et al. 2014) Similarity between attribute values (Yin et al. 2008) Correlated group of attributes (Ba et al. 2015) Heterogeneous data types (Q. Li et al. 2014)... See extensive evaluations of different techniques (X. Li et al. 2012; Waguih and Berti-Equille 2014). General problem far from being solved! 23 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
35 Outline Introduction Truth Finding Probabilistic Databases Uncertainty Management Querying Probabilistic Databases Conclusion 24 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
36 Outline Introduction Truth Finding Probabilistic Databases Uncertainty Management Querying Probabilistic Databases Conclusion 25 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
37 Different types of uncertainty Two dimensions: Different types: Unknown value: NULL in an RDBMS Alternative between several possibilities: either A or B or C Imprecision on a numeric value: a sensor gives a value that is an approximation of the actual value Confidence in a fact as a whole: cf. information extraction Structural uncertainty: the schema of the data itself is uncertain Qualitative (NULL) or Quantitative (95%, low-confidence, etc.) uncertainty 26 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
38 Objective Managing uncertainty Not to pretend this imprecision does not exist, and manage it as rigorously as possible throughout a long, automatic and human, potentially complex, process. 27 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
39 Objective Managing uncertainty Not to pretend this imprecision does not exist, and manage it as rigorously as possible throughout a long, automatic and human, potentially complex, process. Especially: Represent all different forms of uncertainty Use probabilities to represent quantitative information on the confidence in the data Query data and retrieve uncertain results Allow adding, deleting, modifying data in an uncertain way Bonus (if possible): Keep as well lineage/provenance information, so as to ensure traceability 27 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
40 Why probabilities? Not the only option: fuzzy set theory (Galindo et al. 2005), Dempster-Shafer theory (Zadeh 1986) Mathematically rich theory, nice semantics with respect to traditional database operations (e.g., joins) Some applications already generate probabilities (e.g., statistical information extraction or natural language probabilities) In other cases, we cheat and pretend that (normalized) confidence scores are probabilities: see this as a first-order approximation 28 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
41 Outline Introduction Truth Finding Probabilistic Databases Uncertainty Management Querying Probabilistic Databases Conclusion 29 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
42 Tuple-independent databases (TID) S a a 1 b v 0:5 b w 0:2 30 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
43 Tuple-independent databases (TID) S b a a b v 0:5 b w 0:2 a v w 30 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
44 Tuple-independent databases (TID) S b a a b v 0:5 b w 0:2 a v w This TID instance represents the following probability distribution: 30 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
45 Tuple-independent databases (TID) S b a a b v 0:5 b w 0:2 a v w This TID instance represents the following probability distribution: 0:5 0:2 S a b b a v w 30 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
46 Tuple-independent databases (TID) S b a a b v 0:5 b w 0:2 a v w This TID instance represents the following probability distribution: 0:5 0:2 S 0:5 (1 0:2) S a b b a v w a b a v 30 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
47 Tuple-independent databases (TID) S b a a b v 0:5 b w 0:2 a v w This TID instance represents the following probability distribution: 0:5 0:2 S 0:5 (1 0:2) S (1 0:5) 0:2 S a b b a v w a b a v a b a w 30 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
48 Tuple-independent databases (TID) S b a a b v 0:5 b w 0:2 a v w This TID instance represents the following probability distribution: 0:5 0:2 0:5 (1 0:2) (1 0:5) 0:2 (1 0:5) (1 0:2) S S S S a b b a v w a b a v a b a w a a 30 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
49 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
50 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
51 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
52 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
53 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
54 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
55 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
56 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 The query is true iff R(b) is here and one of: 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
57 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 The query is true iff R(b) is here and one of: S(b; v) and T (v) are here 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
58 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 The query is true iff R(b) is here and one of: S(b; v) and T (v) are here S(b; w) and T (w) are here 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
59 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 The query is true iff R(b) is here and one of: S(b; v) and T (v) are here S(b; w) and T (w) are here! Probability: 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
60 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 The query is true iff R(b) is here and one of: S(b; v) and T (v) are here S(b; w) and T (w) are here! Probability: 0:4 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
61 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 The query is true iff R(b) is here and one of: S(b; v) and T (v) are here S(b; w) and T (w) are here! Probability: 0: / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
62 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 The query is true iff R(b) is here and one of: S(b; v) and T (v) are here S(b; w) and T (w) are here! Probability: 0:4 1 (1 0:5 0:3) 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
63 Query evaluation on probabilistic instances We want to evaluate the probability of a query on a TID instance q : 9x y R(x) ^ S(x; y) ^ T (y) R a 1 b 0:4 c 0:6 S a a 1 b v 0:5 b w 0:2 T v 0:3 w 0:7 b 1 The query is true iff R(b) is here and one of: S(b; v) and T (v) are here S(b; w) and T (w) are here! Probability: 0:4 1 (1 0:5 0:3) (1 0:2 0:7) 31 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
64 Complexity of probabilistic query evaluation (PQE) What is the data complexity of probabilistic query evaluation on TID depending on the class Q of queries and class I of instances? 32 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
65 Complexity of probabilistic query evaluation (PQE) What is the data complexity of probabilistic query evaluation on TID depending on the class Q of queries and class I of instances? Existing dichotomy result: (Dalvi and Suciu 2012) Q are (unions of) conjunctive queries, I is all TID instances There is a class S Q of safe queries 32 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
66 Complexity of probabilistic query evaluation (PQE) What is the data complexity of probabilistic query evaluation on TID depending on the class Q of queries and class I of instances? Existing dichotomy result: (Dalvi and Suciu 2012) Q are (unions of) conjunctive queries, I is all TID instances There is a class S Q of safe queries PQE is PTIME for any q 2 S on all instances 32 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
67 Complexity of probabilistic query evaluation (PQE) What is the data complexity of probabilistic query evaluation on TID depending on the class Q of queries and class I of instances? Existing dichotomy result: (Dalvi and Suciu 2012) Q are (unions of) conjunctive queries, I is all TID instances There is a class S Q of safe queries PQE is PTIME for any q 2 S on all instances PQE is #P-hard for any q 2 QnS on all instances 32 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
68 Complexity of probabilistic query evaluation (PQE) What is the data complexity of probabilistic query evaluation on TID depending on the class Q of queries and class I of instances? Existing dichotomy result: (Dalvi and Suciu 2012) Q are (unions of) conjunctive queries, I is all TID instances There is a class S Q of safe queries PQE is PTIME for any q 2 S on all instances PQE is #P-hard for any q 2 QnS on all instances q : 9x y R(x) ^ S(x; y) ^ T (y) is unsafe! 32 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
69 Complexity of probabilistic query evaluation (PQE) What is the data complexity of probabilistic query evaluation on TID depending on the class Q of queries and class I of instances? Existing dichotomy result: (Dalvi and Suciu 2012) Q are (unions of) conjunctive queries, I is all TID instances There is a class S Q of safe queries PQE is PTIME for any q 2 S on all instances PQE is #P-hard for any q 2 QnS on all instances q : 9x y R(x) ^ S(x; y) ^ T (y) is unsafe! Is there a smaller class I such that PQE is tractable for a larger Q? 32 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
70 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
71 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
72 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
73 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
74 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
75 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
76 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
77 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
78 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
79 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
80 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
81 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
82 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
83 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
84 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
85 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
86 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) Trees have treewidth 1 Cycles have treewidth 2 k-cliques and (k 1)-grids have treewidth k 1 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
87 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) Trees have treewidth 1 Cycles have treewidth 2 k-cliques and (k 1)-grids have treewidth k 1! Known results (Courcelle 1990): I: treelike instances; Q: monadic second-order queries! non-probabilistic QE is in linear time 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
88 Trees and treelike instances Idea: let I be treelike instances (constant bound on treewidth) Trees have treewidth 1 Cycles have treewidth 2 k-cliques and (k 1)-grids have treewidth k 1! Known results (Courcelle 1990): I: treelike instances; Q: monadic second-order queries! non-probabilistic QE is in linear time! Does this extend to probabilistic QE? 33 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
89 Dichotomy for PQE An instance-based dichotomy result: Upper bound. (Amarilli et al. 2015) For I the treelike instances and Q the MSO queries! PQE is in linear time modulo arithmetic costs 34 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
90 Dichotomy for PQE An instance-based dichotomy result: Upper bound. (Amarilli et al. 2015) For I the treelike instances and Q the MSO queries! PQE is in linear time modulo arithmetic costs Also for expressive provenance representations Also with bounded-treewidth correlations 34 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
91 Dichotomy for PQE An instance-based dichotomy result: Upper bound. (Amarilli et al. 2015) For I the treelike instances and Q the MSO queries! PQE is in linear time modulo arithmetic costs Also for expressive provenance representations Also with bounded-treewidth correlations Lower bound. (Amarilli et al. 2016) For any unbounded-tw family I and Q the FO queries! PQE is #P-hard under RP reductions assuming: High-tw instances in I are easily constructible Signature arity is 2 (graphs) 34 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
92 Application: Efficient querying of uncertain graphs (Maniu et al. 2014) 6 6 1: : : : : : 0.75 (α) (β) Problem: Optimize query evaluation on probabilistic graphs Challenge: Real graph data is not treelike 6 1: : : 1 3 (γ) (ε) 6 1: : : : : : 0.5 1: (δ) (ζ) Methodology: Build partial tree decompositions and use different query evaluation techniques on treelike parts and on the rest of the data 35 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
93 Outline Introduction Truth Finding Probabilistic Databases Conclusion 36 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
94 Conclusion The real world is uncertain Tools we use to process the real world introduce uncertainty Need for principled methods to: Estimate uncertainty (veracity, truthfulness... ) of information Properly manage the confidence (probability, level of certainty... ) in the information Keep information on the provenance of data 37 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
95 Conclusion The real world is uncertain Tools we use to process the real world introduce uncertainty Need for principled methods to: Estimate uncertainty (veracity, truthfulness... ) of information Properly manage the confidence (probability, level of certainty... ) in the information Keep information on the provenance of data Merci. 37 / 37 Big Data & Market Insights Pierre Senellart École normale supérieure
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