Trio-One: Layering Uncertainty and Lineage on a Conventional DBMS

1. UNCERTAINTY LINEAGE DATA Trio-One:Layering Uncertainty and Lineage on a Conventional DBMS Martin Theobald Jennifer Widom Stanford University

2. Outline • Motivation and Applications • Working Model for ULDBs • Trio-One System Architecture • Efficient Confidence Computations

3. Motivation • Many applications involve data that is uncertain • (approximate, probabilistic, inexact, incomplete, • imprecise, fuzzy, inaccurate, ...) • Many of the same applications need to track the lineage of their data • Neither uncertainty nor lineage are supported by conventional Database Management Systems (DBMSs) Coincidence or Fate?

4. Sample Applications • Deduplication • Uncertainty:Match and merge • Lineage:Source records • Information extraction • Uncertainty:Extracted labels and values • Lineage:Original context • Information integration • Uncertainty:Inconsistent information • Lineage:Original sources

5. Sample Applications • Scientific experiments • Uncertainty: Captured (and derived) data • Lineage: Layers of views • Sensor data • Uncertainty: Sensor values, aggregations, missing readings • Lineage: Original readings, views

6. Claim Coincidence or Fate? • The connection between uncertainty and lineage goes deeper than just a shared need by several applications

7. Lineage and Uncertainty • Lineage... • Enables simple and consistent representation of uncertain data • Allows for intuitive and complete working models • Correlates uncertainty in query results with uncertainty in the input data • Can make computation over uncertain data more efficient • Applications use lineage to reduce or resolve • uncertainty

8. Goal • A new kind of DBMS in which: • Data • Uncertainty • Lineage are all first-class interrelated concepts } Trio

9. The Trio Trio • Data Model • Simplest extension to relational model that’s sufficiently expressive • Query Language • Simple extension to SQL with well-defined semantics and intuitive behavior • System • A complete open-source DBMS that people want to use

10. The Present • Data Model • Uncertainty-Lineage Databases (ULDBs) • Query Language • TriQL • System • Trio-One: Layered prototype deployable on top of any standard relational DBMS

11. Running Example: Crime-Solving • Saw(witness,car) // may be uncertain • Drives(person,car) // may be uncertain • Suspects(person)= πperson(Saw ⋈car Drives)

12. Data Model: Uncertainty • An uncertain database represents a set of • possible instances of data values • Amy saw either a Honda or a Toyota • Jimmy drives a Toyota, a Mazda, or both • Betty saw an Acura with confidence 0.5 or a Toyota with confidence 0.3 • Hank is a suspect with confidence 0.7

13. Our Model for Uncertainty • 1. Alternatives (mutually exclusive) • 2. ‘?’ (Maybe) Annotations • 3. Confidences

14. Our Model for Uncertainty • 1. Alternatives:uncertainty about value • 2. ‘?’ (Maybe) Annotations • 3. Confidences Three possible instances =

15. Our Model for Uncertainty • 1. Alternatives • 2.‘?’ (Maybe): uncertainty about presence • 3. Confidences ? Six possible instances

16. Our Model for Uncertainty • 1. Alternatives • 2. ‘?’ (Maybe) Annotations • 3. Confidences: weighted uncertainty ? Six possible instances, each with a probability

17. Models for Uncertainty • Our model (so far) is not especially new • We spent some time exploring the space of models for uncertainty • Tension between understandability and expressiveness • Our model is understandable • But it is not complete, or even closed under common operations

18. Closure and Completeness • Completeness • Can represent any finite set of possible instances • Closure • Can represent any result of relational operators • Note: Completeness Closure

19. Models for Uncertainty • A-Tuples – Uncertainty on attribute values • (Amy, {Toyota, Mazda}) • Not closed • X-Tuples – Uncertainty on entire tuples • { (Amy, Toyota), (Amy, Mazda) } • Still not closed • C-Tables – Tuples + Boolean constraints • { (Amy, Toyota, X=1), • (Amy, Mazda, X<>1), • (Cathy, Honda, X<>1) } • Closed and complete! • Understandable?

20. Our Model is Not Closed Suspects= πperson(Saw ⋈car Drives) CANNOT Does not correctly capture possible instances in the result ? ? ?

21. to the Rescue Lineage • Lineage (provenance): “where data came from” • Internal lineage • External lineage • In Trio: A functionλ from alternatives to other • alternatives (or external sources)

22. Example with Lineage Correctly captures possible instances in the result Suspects= πperson(Saw ⋈car Drives) λ(31) = (11,2),(21,2) ? λ(32,1) = (11,1),(22,1); λ(32,2) = (11,1),(22,2) ? ? λ(33) = (11,1), 23

23. Trio Data Model Uncertainty-Lineage Databases (ULDBs) • 1. Alternatives (mutually exclusive) • 2. ‘?’ (Maybe) Annotations • 3. Confidences • 4. Lineage • ULDBs are closed and complete

24. ULDBs: Lineage • Conjunctive lineage sufficient for most operations • Disjunctive lineage for duplicate-elimination • Negative lineage for difference

25. ULDBs: Minimality • A ULDB relation R represents a set of possible • instances • Does every tuple inRappear in some possible instance? (no extraneous tuples) • Does every maybe-tuple inRnotappear in some possible instance?(no extraneous ‘?’s) Also Data-minimality Lineage-minimality

26. Data Minimality Examples • Extraneous ‘?’ λ(40,1)=(10,1); λ(40,2)=(10,2) ? extraneous ? ?

27. Data Minimality Examples • Extraneous tuple ? extraneous ? ?

28. ULDBs: Membership Questions • Does a given tuple t appear in some(all)possible instance(s)ofR? • Is a given tableTone of(all of)the possible instances ofR? Polynomial algorithms based on data-minimization NP-Hard

29. Non-Theorists... • Wake Back Up!

30. Querying ULDBs TriQL • Simple extension to SQL • Formal semantics, intuitive meaning • Query uncertainty, confidences, and lineage

31. Initial TriQL Example SELECT Drives.person INTO Suspects FROM Saw, Drives WHERE Saw.car = Drives.car λ(31) = (11,2),(21,2) ? λ(32,1)=(11,1),(22,1); λ(32,2)=(11,1),(22,2) ? ? λ(33) = (11,1), 23

32. Formal Semantics • Query Qon ULDB D implementation of Q D D’ D + Result operational semantics possible instances representation of instances Qon each instance D1, D2, …, Dn Q(D1), Q(D2), …, Q(Dn)

33. Operational Semantics SELECT attr-list [ INTO table ] FROM X1, X2, ..., Xn WHERE predicate • Over conventional relational database: For each tuple in cross-product of X1, X2, ..., Xn • Evaluate the predicate • If true, project attr-list to create result tuple • If INTO clause, insert into table

34. Operational Semantics SELECT attr-list [ INTO table ] FROM X1, X2, ..., Xn WHERE predicate • Over ULDB: For each tuple in cross-product of X1, X2, ..., Xn • Create “super tuple” T from all combinations of alternatives • Evaluate predicate on each alternative in T; keep only the true ones • Project attr-list on each alternative to create result tuple • Details: ‘?’, lineage, confidences

35. Operational Semantics: Example SELECT Drives.person FROM Saw, Drives WHERE Saw.car = Drives.car

36. Operational Semantics: Example SELECT Drives.person FROM Saw, Drives WHERE Saw.car = Drives.car

37. Operational Semantics: Example SELECT Drives.person FROM Saw, Drives WHERE Saw.car = Drives.car

38. Operational Semantics: Example SELECT Drives.person FROM Saw, Drives WHERE Saw.car = Drives.car

39. Operational Semantics: Example SELECT Drives.person FROM Saw, Drives WHERE Saw.car = Drives.car

40. Operational Semantics: Example SELECT Drives.person FROM Saw, Drives WHERE Saw.car = Drives.car

41. Operational Semantics: Example SELECT Drives.person FROM Saw, Drives WHERE Saw.car = Drives.car

42. Operational Semantics: Example SELECT Drives.personINTO Suspects FROM Saw, Drives WHERE Saw.car = Drives.car ? λ( ) = ... λ( ) = ... ?

43. Confidences • Confidences supplied with base data • Trio computes confidences on query results • Default probabilistic interpretation • Can choose to plug in different arithmetic ? ? Probabilistic Min 0.3 0.4 ? 0.6

44. TriQL: Querying Confidences • Built-in function:Conf() • SELECT Drives.person INTO Suspects • FROM Saw, Drives • WHERE Saw.car = Drives.car • AND Conf(Saw) > 0.5 AND Conf(Drives) > 0.8 • SELECT Drives.person INTO Suspects • FROM Saw, Drives • WHERE Saw.car = Drives.car • AND Conf(*) > 0.4

45. TriQL: Querying Lineage • Built-in join predicate:Lineage() • SELECT Saw.witness INTO AccusesHank • FROM Suspects, Saw • WHERE Lineage(Suspects,Saw) • AND Suspects.person = ‘Hank’ • Also works for transitive lineage: • SELECT witness • FROM AccusesHank • WHERE Lineage(Saw,AccusesHank)

46. Additional Query Constructs • “Horizontal subqueries” Refer to tuple alternatives as a relation • Unmerged (horizontal duplicates) • Flatten, GroupAlts • NoLineage, NoConf, NoMaybe • Query-computed confidences • Data modification statements

47. Final Example Query Credibility • List suspects with conf values based on accuser credibility

48. Final Example Query Credibility SELECT suspect, score/[sum(score)] as conf FROM (SELECT suspect, (SELECT score FROM Credibility C WHERE C.person = P.accuser) FROM PrimeSuspect P)

49. Final Example Query Credibility SELECT suspect, score/[sum(score)] as conf FROM (SELECT suspect, (SELECT score FROM Credibility C WHERE C.person = P.accuser) FROM PrimeSuspect P)

50. Final Example Query Credibility SELECT suspect, score/[sum(score)]as conf FROM (SELECT suspect, (SELECT score FROM Credibility C WHERE C.person = P.accuser) FROM PrimeSuspect P) “Scaled as conf” “Uniform as conf” …