Supporting Queries with Imprecise Constraints Ullas Nambiar Dept. of Computer Science University of California, Davis Subbarao Kambhampati Dept. of Computer

Supporting Queries with Imprecise Constraints

Ullas NambiarDept. of Computer Science

University of California, Davis

Subbarao Kambhampati

Dept. of Computer ScienceArizona State University

18th July, AAAI -06, Boston, USA

[WebDB 2004; VLDB 2005 (d);WWW 2005 (p); ICDE 2006]


Dichotomy in Query Processing

Databases

• User knows what she wants

• User query completely expresses the need

• Answers exactly matching query constraints

IR Systems

• User has an idea of what she wants

• User query captures the need to some degree

• Answers ranked by degree of relevance

AutonomousUn-curated DB

Inexperienced,Impatient user population

http://www.asu.edu/


Why Support Imprecise Queries ?

Want a ‘sedan’ priced around $7000

A Feasible Query

Make =“Toyota”, Model=“Camry”,

Price ≤ $7000

What about the price of a Honda Accord?

Is there a Camry for $7100?

Solution: Support Imprecise Queries

………

1998$6500CamryToyota




http://www.asu.edu/


Others are following …

http://www.asu.edu/


The Problem: Given a conjunctive query Q over a relation R, find a set of tuples that will be considered relevant by the user.

Ans(Q) ={x|x Є R, Rel(x|Q,U) >c}

Constraints– Minimal burden on the end user – No changes to existing database – Domain independent

What does Supporting Imprecise Queries Mean?

AutonomousUn-curated DB

Inexperienced,Impatient user population

http://www.asu.edu/


Assessing Relevance Function Rel(x|Q,U)

We looked at a variety of non-intrusive relevance assessment methods– Basic idea is to learn the relevance function for user

population rather than single users Methods

– From the analysis of the (sample) data itself • Allows us to understand the relative importance of attributes,

and the similarity between the values of an attribute [ICDE 2006;WWW 2005 poster]

– From the analysis of query logs• Allows us to identify related queries, and then throw in their

answers [WIDM 2003; WebDB 2004]

– From co-click patterns• Allows us to identify similarity based on user click pattern

[Under Review]

http://www.asu.edu/


Our Solution: AIMQ

http://www.asu.edu/


The AIMQ Approach

ImpreciseQuery

Q

Query Engine

Map: Convert“like” to “=”

Qpr = Map(Q)

Dependency Miner

Use Base Set as set ofrelaxable selection

queries

Using AFDs findrelaxation order

Derive Extended Set byexecuting relaxed queries

Similarity Miner

Use Value similaritiesand attribute

importance to measuretuple similarities

Prune tuples belowthreshold

Return Ranked Set

Query Engine

Derive BaseSet Abs

Abs = Qpr(R)

[For the special case of empty query, we start with a relaxation that uses AFD analysis]

http://www.asu.edu/


An Illustrative Example

ImpreciseQuery

Q Map: Convert“like” to “=”

Qpr = Map(Q)

Use Base Set as set ofrelaxable selectionqueries



Use Concept similarityto measure tuplesimilarities


Return Ranked Set

Derive BaseSet Abs

Abs = Qpr(R)

Relation:- CarDB(Make, Model, Price, Year) Imprecise query

Q :− CarDB(Model like “Camry”, Price like “10k”)

Base query

Qpr :− CarDB(Model = “Camry”, Price = “10k”)

Base set Abs

Make = “Toyota”, Model = “Camry”, Price = “10k”, Year = “2000”Make = “Toyota”, Model = “Camry”, Price = “10k”, Year = “2001”

http://www.asu.edu/


Obtaining Extended Set

ImpreciseQuery


Qpr = Map(Q)






Return Ranked Set

Derive BaseSet Abs

Abs = Qpr(R)

Problem: Given base set, find tuples from database similar to tuples in base set.

Solution: – Consider each tuple in base set as a selection query.

e.g. Make = “Toyota”, Model = “Camry”, Price = “10k”, Year = “2000”

– Relax each such query to obtain “similar” precise queries.e.g. Make = “Toyota”, Model = “Camry”, Price = “”, Year =“2000”

– Execute and determine tuples having similarity above some threshold.

Challenge: Which attribute should be relaxed first?

– Make ? Model ? Price ? Year ?

Solution: Relax least important attribute first.

http://www.asu.edu/

Least Important Attribute

Definition: An attribute whose binding value when changed has minimal effect on values binding other attributes.• Does not decide values of other attributes• Value may depend on other attributes

E.g. Changing/relaxing Price will usually not affect other attributes but changing Model usually affects Price

Dependence between attributes useful to decide relative importance• Approximate Functional Dependencies & Approximate Keys

Approximate in the sense that they are obeyed by a large percentage (but not all) of tuples in the database• Can use TANE, an algorithm by Huhtala et al [1999]


Deciding Attribute Importance Mine AFDs and Approximate

Keys Create dependence graph using

AFDs– Strongly connected hence a

topological sort not possible Using Approximate Key with

highest support partition attributes into

– Deciding set– Dependent set– Sort the subsets using

dependence and influence weights

Measure attribute importance as

ImpreciseQuery


Qpr = Map(Q)






Return Ranked Set

Derive BaseSet Abs

Abs = Qpr(R)

CarDB(Make, Model, Year, Price)

Decides: Make, YearDepends: Model, Price

Order: Price, Model, Year, Make

1- attribute: { Price, Model, Year, Make}

2-attribute: {(Price, Model), (Price, Year), (Price, Make).. }

•Attribute relaxation order is all non-keys first then keys

•Greedy multi-attribute relaxation

depends

idepends

decides

idecides

iimp

Wt

AWt

or

Wt

AWt

RAttributescount

AlaxOrderAiW

)(

)(

))((

)(Re)(

http://www.asu.edu/

Tuple Similarity

Tuples obtained after relaxation are ranked according to their

similarity to the corresponding tuples in base set

where Wi = normalized influence weights, ∑ Wi = 1 , i = 1 to |Attributes(R)|

Value Similarity• Euclidean for numerical attributes e.g. Price, Year• Concept Similarity for categorical e.g. Make, Model

WiAitvalueAitvalueilarityAttrSimttSimilarity ]))[2(]),[1(()2,1(

ImpreciseQuery


Qpr = Map(Q)






Return Ranked Set

Derive BaseSet Abs

Abs = Qpr(R)


Categorical Value Similarity Two words are semantically

similar if they have a common context – from NLP

Context of a value represented as a set of bags of co-occurring values called Supertuple

Value Similarity: Estimated as the percentage of common {Attribute, Value} pairs

– Measured as the Jaccard Similarity among supertuples representing the values

ST(QMake=Toy

ota)

Model Camry: 3, Corolla: 4,….

Year 2000:6,1999:5 2001:2,……

Price 5995:4, 6500:3, 4000:6

Supertuple for Concept Make=Toyota

JaccardSim(A,B) = BABA

m

i

imp AivSTAivSTJaccardSimAiWvvVSim1

)).2(,).1(()()2,1(

ImpreciseQuery


Qpr = Map(Q)






Return Ranked Set

Derive BaseSet Abs

Abs = Qpr(R)

http://www.asu.edu/

August 15th 2005 Answering Imprecise Queries over Autonomous Databases

Value Similarity Graph

Ford

Chevrolet

Toyota

Honda

DodgeNissan

BMW

0.25

0.16

0.110.15

0.12

0.22


Empirical Evaluation Goal

– Evaluate the effectiveness of the query relaxation and similarity estimation

Database– Used car database CarDB based on Yahoo AutosCarDB( Make, Model, Year, Price, Mileage, Location, Color)

• Populated using 100k tuples from Yahoo Autos

– Census Database from UCI Machine Learning Repository• Populated using 45k tuples

Algorithms – AIMQ

• RandomRelax – randomly picks attribute to relax• GuidedRelax – uses relaxation order determined using approximate keys

and AFDs

– ROCK: RObust Clustering using linKs (Guha et al, ICDE 1999)• Compute Neighbours and Links between every tuple

Neighbour – tuples similar to each other Link – Number of common neighbours between two tuples

• Cluster tuples having common neighbours

http://www.asu.edu/


Efficiency of Relaxation

0

100

200

300

400

500

600

700

800

900

1 2 3 4 5 6 7 8 9 10

Queries

Wor

k/Re

leva

nt T

uple

Є= 0.7

Є = 0.6

Є = 0.5

•Average 8 tuples extracted per relevant tuple for Є =0.5. Increases to 120 tuples for Є=0.7.

•Not resilient to change in Є

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10Queries

Wor

k/R

elev

ant T

uple

Є = 0.7

Є = 0.6

Є = 0.5

•Average 4 tuples extracted per relevant tuple for Є=0.5. Goes up to 12 tuples for Є= 0.7.

•Resilient to change in Є

Random Relaxation Guided Relaxation

http://www.asu.edu/


Accuracy over CarDB

•14 queries over 100K tuples

• Similarity learned using 25k sample

• Mean Reciprocal Rank (MRR) estimated as

• Overall high MRR shows high relevance of suggested answers

1|)()(|

1)(

ii tAIMQRanktUserRankAvgQMRR

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14Queries

Avera

ge M

RR .

GuidedRelax

RandomRelax

ROCK

http://www.asu.edu/


Handling Imprecision & Incompleteness

Incompleteness in data– Databases are being

populated by• Entry by lay people• Automated extraction

E.g. entering an “accord” without mentioning “Honda”

Imprecision in queries– Queries posed by lay users

• Who combine querying and browsing

General Solution: “Expected Relevance Ranking”

Relevance Function

DensityFunction

Challenge: Automated & Non-intrusive assessment of Relevance and Density functions

http://www.asu.edu/


Handling Imprecision & Incompleteness

http://www.asu.edu/

Documents

Supporting Queries with Imprecise Constraints Ullas Nambiar Dept. of Computer Science University of California, Davis Subbarao Kambhampati Dept. of Computer