Trio-One: Layering Uncertainty and Lineage on a Conventional DBMS Martin Theobald Jennifer Widom Stanford University

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

Martin TheobaldJennifer 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 / Entity Resolution• 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

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Claim

The connection between uncertainty and lineage goes deeper than just a shared need by several applications

Coincidence or Fate?

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 confidence computations over

uncertain data more efficient

Applications use lineage to reduce or resolve uncertainty

8

Goal

A new kind of DBMS in which:1. Data2. Uncertainty3. Lineage

are all first-class interrelated concepts

Trio }

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The Trio Trio

1. Data Model Simplest extension to relational model that’s

sufficiently expressive

2. Query Language Simple extension to SQL with well-defined

semantics and intuitive behavior

3. System A complete open-source DBMS that people

want to use

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The Present

1. Data Model Uncertainty-Lineage Databases (ULDBs)

2. Query Language TriQL

3. System Trio-One: Layered prototype deployable

on top of any standard relational DBMS

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Running Example: Crime-Solving

Saw(witness,car) // may be uncertainDrives(person,car) // may be uncertain

Suspects(person) = πperson(Saw ⋈car Drives)

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Data Model: Uncertainty

An uncertain database represents a set ofpossible 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

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Our Model for Uncertainty

1. Alternatives (mutually exclusive)2. ‘?’ (Maybe) Annotations3. Confidences

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1. Alternatives: uncertainty about data value(s)

2. ‘?’ (Maybe) Annotations3. Confidences

Saw (witness,car)(Amy, Honda) ∥ (Amy, Toyota) ∥ (Amy,

Mazda)

witness carAmy { Honda, Toyota,

Mazda }=

Three possibleinstances

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Six possibleinstances


1. Alternatives2. ‘?’ (Maybe): uncertainty about presence3. Confidences

Saw (witness,car)(Amy, Honda) ∥ (Amy, Toyota) ∥ (Amy,

Mazda)(Betty, Acura)

?

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1. Alternatives2. ‘?’ (Maybe) Annotations3. Confidences: weighted uncertainty

Saw (witness,car)(Amy, Honda): 0.5 ∥ (Amy,Toyota): 0.3 ∥ (Amy,

Mazda): 0.2(Betty, Acura): 0.6

?

Six possible instances, each with a probability

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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

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Closure and Completeness

Completeness Can represent any finite set of possible

instancesClosure Can represent any result of relational

operators

Note: Completeness Closure

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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?

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Our Model is Not Closed

Saw (witness,car)(Cathy, Honda) ∥ (Cathy,

Mazda)

Drives (person,car)(Jimmy, Toyota) ∥ (Jimmy,

Mazda)(Billy, Honda) ∥ (Frank, Honda)

(Hank, Honda)

SuspectsJimmy

Billy ∥ FrankHank

Suspects = πperson(Saw ⋈car Drives)

???

Does not correctlycapture possibleinstances in theresult

CANNOT

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to the Rescue

Lineage (provenance): “where data came from”• Internal lineage – pointers to base data• External lineage – files, URLs, web portals, etc.

In Trio: A Boolean function λ from alternatives to other alternatives (or external sources)

Lineage

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Example with Lineage

ID Saw (witness,car)11

(Cathy, Honda) ∥ (Cathy, Mazda)

ID Drives (person,car)21

(Jimmy, Toyota) ∥ (Jimmy, Mazda)

22

(Billy, Honda) ∥ (Frank, Honda)

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(Hank, Honda)

ID Suspects31

Jimmy

32

Billy ∥ Frank

33

Hank

???

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

Correctly captures possible instances inthe result

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Trio Data Model

1. Alternatives (mutually exclusive) 2. ‘?’ (Maybe) Annotations 3. Confidences 4. Lineage

ULDBs are closed and complete

Uncertainty-Lineage Databases (ULDBs)

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ULDBs: Lineage

Conjunctive lineage sufficient for most operations• Disjunctive lineage for duplicate-elimination• Negative lineage for difference

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ULDBs: Minimality

A ULDB relation R represents a set of possible

instancesDoes every tuple in R appear in some

possible instance? (no extraneous tuples)

Does every maybe-tuple in R not appear in some possible instance? (no extraneous ‘?’s)

Also

Data-minimality

Lineage-minimality

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Data Minimality ExamplesExtraneous ‘?’

. . .

10


. . .

. . .

40

Billy ∥ Frank

. . .

?λ(40,1)=(10,1); λ(40,2)=(10,2)extraneous

. . .

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(Billy, Honda)

. . .

?. . .

30

(Frank, Honda)

. . .

?

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Data Minimality ExamplesExtraneous tuple

(Diane, Mazda) ∥ (Diane, Acura)

Dianeextraneous

(Diane, Mazda)

(Diane, Acura)

?

??

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ULDBs: Membership Questions

Does a given tuple t appear in some (all) possible instance(s) of R ?

Is a given table T one of (all of) the possible instances of R ?

Polynomial algorithms based on data-minimization

NP-Hard

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Non-Theorists...

Wake Back Up!

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Querying ULDBs

• Simple extension to SQL• Formal semantics, intuitive meaning• Query uncertainty, confidences, and

lineage

TriQL

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Initial TriQL Example

ID Saw (witness,car)11

(Cathy, Honda) ∥ (Cathy, Mazda)

ID Drives (person,car)21

(Jimmy, Toyota) ∥ (Jimmy, Mazda)

22


23

(Hank, Honda)SELECT Drives.person INTO SuspectsFROM Saw, DrivesWHERE Saw.car = Drives.car

ID Suspects31

Jimmy

32

Billy ∥ Frank

33

Hank

???

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

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Formal Semantics

Query Q on ULDB D

D

D1, D2, …, Dn

possibleinstances

Q on eachinstance

representationof instances

Q(D1), Q(D2), …, Q(Dn)

D’implementation of Q

operational semanticsD + Result

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Operational Semantics

Over conventional relational database:For each tuple in cross-product of X1, X2, ..., Xn

1. Evaluate the predicate2. If true, project attr-list to create result tuple3. If INTO clause, insert into table

SELECT attr-list [ INTO table ]FROM X1, X2, ..., XnWHERE predicate

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Operational Semantics

Over ULDB:For each tuple in cross-product of X1, X2, ..., Xn

1. Create “super tuple” T from all combinations of alternatives

2. Evaluate predicate on each alternative in T ; keep only the true ones

3. Project attr-list on each alternative to create result tuple

4. Details: ‘?’, lineage, confidences

SELECT attr-list [ INTO table ]FROM X1, X2, ..., XnWHERE predicate

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Operational Semantics: Example

SELECT Drives.personFROM Saw, DrivesWHERE Saw.car = Drives.car


Mazda)

Drives (person,car)(Jim, Mazda) ∥ (Bill, Mazda)

(Hank, Honda)

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Mazda)


(Hank, Honda)

(Cathy,Honda,Jim,Mazda)∥(Cathy,Honda,Bill,Mazda)∥(Cathy,Mazda,Jim,Mazda)∥(Cathy,Mazda,Bill,Mazda)

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Mazda)


(Hank, Honda)


38




Mazda)


(Hank, Honda)


39





Mazda)


(Hank, Honda)

(Cathy,Honda,Hank,Honda) ∥ (Cathy,Mazda,Hank,Honda)

40





Mazda)


(Hank, Honda)


41





Mazda)


(Hank, Honda)


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SELECT Drives.person INTO SuspectsFROM Saw, DrivesWHERE Saw.car = Drives.car


Mazda)


(Hank, Honda)

SuspectsJim ∥ Bill

Hank??

λ( ) = ...λ( ) = ...

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Confidences

Confidences supplied with base dataTrio computes confidences on query results

• Default probabilistic interpretation• Can choose to plug in different arithmetic

Saw (witness,car)(Cathy, Honda): 0.6 ∥ (Cathy,

Mazda): 0.4

Drives (person,car)(Jim, Mazda): 0.3 ∥ (Bill, Mazda):

0.6(Hank, Honda) ): 1.0

SuspectsJim: 0.12 ∥ Bill: 0.24

Hank: 0.6??

?

0.3 0.4 0.6

Probabilistic Min

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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

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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)

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Additional Query Constructs

• “Horizontal subqueries”Refer to tuple alternatives as a relation

• Unmerged (allow horizontal duplicates)• Flatten, GroupAlts

• NoLineage, NoConf, NoMaybe

• Query-computed confidences• SQL-like data modification statements

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Final Example Query

PrimeSuspect (crime#, accuser, suspect)(1, Amy, Jimmy) ∥ (1, Betty, Billy) ∥ (1, Cathy,

Hank)(2, Cathy, Frank) ∥ (2, Betty, Freddy)

person score

Amy 10Betty 15Cathy 5

SuspectsJimmy: 0.33 ∥ Billy: 0.5 ∥ Hank: 0.166

Frank: 0.25 ∥ Freddy: 0.75

Credibility

List suspects with conf values based on accuser credibility

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Final Example Query



person score




Credibility

SELECT suspect, score/[sum(score)] as confFROM (SELECT suspect, (SELECT score FROM Credibility C WHERE C.person = P.accuser) FROM PrimeSuspect P)

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Final Example Query



person score




Credibility


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Final Example Query



person score




Credibility


“Scaled as conf”

“Uniform as conf”

…

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The Trio System

Version 1Entirely on top of a conventional DBMSSurprisingly easy and complete, reasonably

efficient

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The Trio System: Version 1

Lin:RaidF

r tableaidT

o

R aid xid C

Relational DBMS

create trio table T(A,B)select C into R ...

TrioMetadat

a

Trio APISQL commands

• Result cursors• Traverse lineage

T aid xid A B

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Relation Encoding

aid xid

conf

person

car

21 1 2 Jim Mazda22 1 2 Bill Mazda23 2 1 Hank Honda

SuspectsJim ∥ Bill

Hank

aid xid conf person

31 1 3 Jim32 1 3 Bill33 2 2 Hank


Mazda)


(Hank, Honda)

aid xid conf witness

car

11 1 2 Cathy Honda12 1 2 Cathy Mazda

??

aidFr

table aidTo

31 Saw 1231 Drives 2132 Saw 1232 Drives 2233 Saw 1133 Drives 23

Saw Drives

SuspectsLin:Suspects

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Relation Encoding with Confidences

aid xid

conf

person car

21 1 0.3 Jim Mazda22 1 0.6 Bill Mazda23 2 1.0 Hank Honda

aid xid conf person

31 1 NULL Jim32 1 NULL Bill33 2 NULL Hank

Saw (witness,car)(Cathy, Honda): 0.6 ∥ (Cathy,

Mazda): 0.4

Drives (person,car)(Jim, Mazda): 0.3 ∥ (Bill, Mazda):

0.6(Hank, Honda)

aid xid conf witness

car

11 1 0.6 Cathy Honda12 1 0.4 Cathy Mazda

Saw Drives

Suspects

0.12

0.24

0.6

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Query TranslationPersistent results: Query Q into result table R

1. Run query Q’ to produce “super-result” R Q’ ≈ Q but adds aid/xid’s of source tuples, joins lineage tables for lineage() predicates

2. Group R into alternatives, generate new xid’s3. Materialze lineage data into lin:R4. Compute confidences? (optional)5. Add/update metadata: schemas, confidence info, lineage structure

Transient results: stop at 2, return cursor over new xid’s

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R aid xid C

Relational DBMS

create trio table T(A,B)select C into R ...

TrioMetadat

a

Trio APISQL commands

• Result cursors• Traverse lineage

T aid xid A B

Lin:RaidF

r tableaidT

o

57


Trio API and translator(TriQL parser in Python)

TrioMetadat

a

TrioExplorer(GUI client)

Trio Stored

Procedures

EncodedData

TablesLineageTables

Standard SQL

• Data & system columns• A-IDs for alternatives• “Verticalized” through shared X-IDs• Confidences

• One lineage table per derived table• Connecting A-IDs

• Table types• Schema-level lineage structure

• conf()• lineage()

• TriQL queries• DDL commands• Schema browsing• Table browsing• Explore lineage• On-demand confidence computation

Command-lineclient

Relational DBMS

SPI-Plugin for

PostgreSQLReplacing

“Fetch-All”

58


Trio API and translator

TrioExplorer(GUI client)Command-line

client

Trio DBMSSpecialized

Trio Data Structures

SpecializedTrio Processing & Optimizing

Standard SQL Direct function calls

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Efficient Confidence Computation

Previous approach (probabilistic databases)• Each operator computes confidences during

query execution• Only certain (“safe”) query plans allowed

In ULDBs Confidence of alternative A is function of

confidences in λ(A)

Our approach• Decoupled data and confidence computation• Allow any query plan for data computation• Compute confidences on-demand based on

lineage

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CIDs & Confidence Memoization

Identify set of Closest Independent Descendants (CIDs) for each relation in the schema-level lineage DAG relations with no shared ancestors

Batched confidence computations in SQL• Select unions of distinct base alternatives from

all root-to-leaf lineage paths• With CIDs and memoization enabled

– if confidences are memoized then stop at CIDs – else traverse down to the leafs (base data) and memoize at CIDs

(ongoing work)

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“Probabilistic TPC-H” Setup

• Horizontal split of TPC-H tables

• Uniform-random number of alternatives [1-10]

• Uniform confidences

PartsuppsLineitemsOrders

O2O1

O L P

OL LP

OLP1.5M

1.0M 0.1M

1.0M 0.5M 0.7M

O3 L2L1 L3 L4 P2P1 P3

O L P

CID(OLP) = {O, L, P}

0.8M6M1.5M

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Confidence Computation Times

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

Exec

utio

n Ti

me

(sec

onds

)

O L P OL LP OLP Total

No CIDs

CIDs

63

Per-Tuple vs. Batching (no CIDs)

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Memoization & Join Multiplicity

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Current Topics

System• Full query language• Nice interface• Performance experiments• Demo applications

Algorithms: confidence & lineage computation,

extraneous data, membership questions• Minimize lineage traversal• Confidence memoization• Efficient batch computations

66

Future Directions

Theory, Model, Algorithms• Unlimited opportunities

System• Storage, indexing, partitioning• Statistics and query optimization

More features• Top-k by confidence • Incomplete relations; continuous uncertainty;

correlated uncertainty• External lineage; update lineage; versioning

Search “stanford trio”Current Trio team:

Parag Agrawal, Anish Das Sarma, Raghotham Murthy, Michi Mutsuzaki, Shubha Nabar, Tomoe

Sugihara, Martin Theobald, Jennifer Widom

Special thanks to:Ashok Chandra, Alon Halevy, Jeff Ullman,

Omar Benjelloun

but don’t forgetthe lineage…

Documents

Trio-One: Layering Uncertainty and Lineage on a Conventional DBMS Martin Theobald Jennifer Widom Stanford University