Querying and Updating Probabilistic Information in XML

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Querying and Updating Probabilistic Information in XML

Serge Abiteboul Pierre Senellart

EDBT 2006 March 28th, 2006

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Introduction Imprecise data

Imprecise data

Many tasks generateimprecisedata, with someconfidencevalue:

Information Extraction

Natural Language Processing Data Cleaning

Schema Matching . . .

Need for a way to manage this imprecision, to work with it throughout an entire complex process.

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Imprecise data

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Imprecise data

Natural Language Processing

Data Cleaning Schema Matching . . .

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Imprecise data

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Imprecise data

Schema Matching

. . .

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Imprecise data

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Imprecise data

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Introduction A Probabilistic XML Warehouse

A Probabilistic XML Warehouse

Query interface (tree-pattern with

join) Update interface

(insertions, deletions)

Probabilistic XML Warehouse

Module 1transaction^Update

}

Module 2 Module 3 + confidence

+ confidence

Query Results

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Framework

Outline

1 Introduction

2 Framework Data Trees Queries Updates

3 Possible Worlds Model

4 Fuzzy Tree Model

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Framework Data Trees

Data Trees

Finite,unordered, trees.

No distinction betweenattributeand element nodes. Nomixedcontent.

A

B B E D

foo foo C F

b a r

n e e

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Data Trees

No distinction betweenattributeand element nodes.

Nomixedcontent.

A

B B E D

foo foo C F n e e

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Data Trees

No distinction betweenattributeand element nodes.

Nomixedcontent.

A

B B E D

foo foo C F

b a r

n e e

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Framework Queries

Tree-Pattern With Join Queries

Queries: Tree-Pattern With Join(TPWJ) (standard subset of XQuery)

Join: by value

Result: minimal subtree containing all the nodes mapped by the query

A

B C

+

D

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Framework Queries

Tree-Pattern With Join Queries

Join: by value

A

B C

+

D

val

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Framework Queries

Tree-Pattern With Join Queries

Join: by value

A

B C

+

D

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Framework Updates

Update Transactions

Setof elementary operations:

Insertionsof subtrees Deletionsof subtrees

Update Transaction: TPWJ query + mapping, statingwhereto perform operations.

Probabilistic update: update +confidence

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Framework Updates

Update Transactions

Insertionsof subtrees

Deletionsof subtrees

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Framework Updates

Update Transactions

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Framework Updates

Update Transactions

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Framework Updates

Update Transactions

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Possible Worlds Model

Outline

1 Introduction

2 Framework

3 Possible Worlds Model Model

Semantic Foundation

4 Fuzzy Tree Model

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Possible Worlds Model Model

Possible Worlds Model

Semantic foundationfor probabilistic data: possible worlds model.

Set oftree/probability pairs, one for eachpossible world.

A

C

A

C

D

A

B C

A

B C

D

P =0.06 P =0.14 P =0.24 P =0.56

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Possible Worlds Model Model

Possible Worlds Model

Semantic foundationfor probabilistic data: possible worlds model.

Set oftree/probability pairs, one for eachpossible world.

A

C

A

C

D

A

B C

A

B C

D

P =0.06 P =0.14 P =0.24 P =0.56

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Possible Worlds Model Semantic Foundation

Queries, Updates: Semantic Foundation

Definition

IfT ={(t_i,p_i)}, the result of queryQover the Possible Worlds setT is the normalization of{(t,p_i)|t ∈Q(t_i)}

Definition

The result of an updatet with confidencec on a Possible Worlds setT is the normalization of:

{(t,p)∈T |tis not selected by Q} S {(τ(t),p·c)|t is selected by Q} S {(t,p·(1−c))|t is selected by Q}

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Possible Worlds Model Semantic Foundation

Queries, Updates: Semantic Foundation

Definition

IfT ={(t_i,p_i)}, the result of queryQover the Possible Worlds setT is the normalization of{(t,p_i)|t ∈Q(t_i)}

Definition

The result of an updatet with confidencec on a Possible Worlds setT is the normalization of:

{(t,p)∈T |tis not selected by Q} S {(τ(t),p·c)|t is selected by Q} S {(t,p·(1−c))|t is selected by Q}

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Fuzzy Tree Model

Outline

1 Introduction

2 Framework

4 Fuzzy Tree Model

Model and Possible Worlds Semantics Queries

Updates

Implementation

5 Conclusion

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Fuzzy Tree Model Model and Possible Worlds Semantics

Fuzzy Trees

Data tree withevent conditions(conjunction of probabilistic events or negations of probabilistic events)assigned to each node.

A

B w 1 , ¬ w 2

C

D w 2

Event Proba.

w1 0.8

w2 0.7

semantics

−→

A

C

A

C

D

A

B C

P=0.06 P=0.70 P=0.24

Theorem

The fuzzy tree model is as expressive as the Possible Worlds model.

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Fuzzy Trees

A

B w 1 , ¬ w 2

C

D w 2

Event Proba.

w1 0.8

w2 0.7

semantics

−→

A

C

A

C

D

A

B C

P=0.06 P=0.70 P=0.24

Theorem

The fuzzy tree model is as expressive as the Possible Worlds model.

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Fuzzy Trees

A

B w 1 , ¬ w 2

C

D w 2

Event Proba.

w1 0.8

w2 0.7

semantics

−→

A

C

A

C

D

A

B C

P=0.06 P=0.70 P=0.24

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Fuzzy Tree Model Queries

Queries on Fuzzy Trees

Definition

Queries on fuzzy trees:

Queryon underlying tree.

Probabilities: probability of the conjunction of the conditions of nodes of the mapping.

Theorem

Fuzzy Tree Fuzzy Tree

Possible Worlds Possible Worlds

query

semantics semantics

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Fuzzy Tree Model Queries

Queries on Fuzzy Trees

Definition

Queries on fuzzy trees:

Queryon underlying tree.

Probabilities: probability of the conjunction of the conditions of nodes of the mapping.

Theorem

Fuzzy Tree ^query Fuzzy Tree

semantics semantics

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Fuzzy Tree Model Updates

Updates on Fuzzy Trees

Insertions: no problem. Conditions required for the query to match added to inserted nodes.

Deletions: ok, but more problematic. May yield an exponential growth of the fuzzy tree in case of complex dependencies.

Theorem

update

semantics semantics

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Updates on Fuzzy Trees

Theorem

update

semantics semantics

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Updates on Fuzzy Trees

Theorem

update

semantics semantics

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Example: Conditional Replacement

Replacement ofCbyDifBis present, with confidence 0.9.

A

B w 1

C w 2

Event Proba.

w1 0.8

w2 0.7

A

B

w1

C

¬w1,w2

C

w1,w2,¬w3

D

w1,w2,w3

Event Proba.

w1 0.8

w2 0.7

w3 0.9

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Example: Conditional Replacement

Replacement ofCbyDifBis present, with confidence 0.9.

A

B w 1

C w 2

Event Proba.

w1 0.8

w2 0.7

A

B

w1

C

¬w1,w2

C

w1,w2,¬w3

D

w1,w2,w3

Event Proba.

w1 0.8

w2 0.7

w3 0.9

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Fuzzy Tree Model Implementation

Implementation

Java-based

File system storage (will look at an XML DB next) Query evaluation: Qizx/open XQuery engine Updates expressed in XUpdate

Available freely at

http://pierre.senellart.com/software/fuzzyxml/ cf demo

http://pierre.senellart.com/software/fuzzyxml/demo/

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Implementation

Java-based

File system storage (will look at an XML DB next)

Query evaluation: Qizx/open XQuery engine Updates expressed in XUpdate

Available freely at

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Implementation

Java-based

File system storage (will look at an XML DB next) Query evaluation: Qizx/open XQuery engine

Updates expressed in XUpdate Available freely at

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Implementation

Java-based

Available freely at

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Implementation

Java-based

Available freely at

http://pierre.senellart.com/software/fuzzyxml/

cf demo

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Implementation

Java-based

Available freely at

http://pierre.senellart.com/software/fuzzyxml/

cf demo

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Conclusion

Outline

1 Introduction

2 Framework

4 Fuzzy Tree Model

5 Conclusion Summary

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Conclusion Summary

Summary

A model for representingprobabilisticinformation for semi-structureddata.

Soundandcompletesupport for an important subset of XQuery. Soundandcompletesupport for XUpdate-based transactions with inserts and deletes.

An implementation based on compilation to XQuery/XUpdate.

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Conclusion Summary

Summary

Soundandcompletesupport for an important subset of XQuery.

Soundandcompletesupport for XUpdate-based transactions with inserts and deletes.

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Conclusion Summary

Summary

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Conclusion Summary

Summary

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Conclusion Perspectives

Perspectives

Complexity analysis: query, update, simplification.

Queryoptimization. Fuzzy datasimplification.

Extensions: negation, some limited order.

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Perspectives

Queryoptimization.

Fuzzy datasimplification.

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Perspectives

Queryoptimization.

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Perspectives

Queryoptimization.