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Probabilistic Ranking of Database Query Results

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Probabilistic Ranking of Database Query Results

Surajit Chaudhuri, Microsoft Research

Gautam Das, Microsoft Research

Vagelis Hristidis, Florida International University

Gerhard Weikum, MPI Informatik

Presented by Weimin He

Motivation

Problem Definition

System Architecture

Construction of Ranking Function

Implementation

Experiments

Conclusion and open problems

Weimin He [email protected]

Realtor DB:

Table D=(TID, Price , City, Bedrooms, Bathrooms, LivingArea, SchoolDistrict, View, Pool, Garage, BoatDock)

SQL query:

Select * From D

Where City=Seattle AND View=Waterfront

Weimin He [email protected]

- Many-answers problem
- Two alternative solutions:
Query reformulation

Automatic ranking

- Apply probabilistic model in IR to DB tuple ranking

Weimin He [email protected]

Given a database table D with n tuples {t1, …, tn} over a set of m categorical attributes A = {A1, …, Am}

and a query Q: SELECT * FROM D

WHERE

X1=x1 AND … AND Xs=xs

where each Xi is an attribute from A and xi is a value in its domain.

The set of attributes X ={X1, …, Xs} is known as the set of attributes specified by the query, while the set Y = A – X is known as the set of unspecified attributes

Let be the answer set of Q

How to rank tuples in S and return top-k tuples to the user ?

Weimin He [email protected]

Weimin He [email protected]

- Select * From D Where City=“Seattle” And View=“Waterfront”
Score of a Result Tuple t depends on

- Global Score: Global Importance of Unspecified Attribute Values
- E.g., Homes with good school districts are globally desirable

- Conditional Score: Correlations between Specified and Unspecified Attribute Values
- E.g., Waterfront BoatDock

Weimin He [email protected]

- Bayes’ Rule
- Product Rule

- Document t, Query QR: Relevant document setR = D - R: Irrelevant document set

Weimin He [email protected]

- Tuple t is considered as a document
- Partition t into t(X) and t(Y)
- t(X) and t(Y) are written as X and Y
- Derive from initial scoring function until final ranking function is obtained

Weimin He [email protected]

Weimin He [email protected]

- Given a query Q and a tuple t, the X (and Y) values within themselves are assumed to be independent, though dependencies between the X and Y values are allowed

Weimin He [email protected]

Weimin He [email protected]

Assume a collection of “past” queries existed in system

Workload W is represented as a set of “tuples”

Given query Q and specified attribute set X, approximate R as all query “tuples” in W that also request for X

All properties of the set of relevant tuple set R can be obtained by only examining the subset of the workload that caontains queries that also request for X

Weimin He [email protected]

Weimin He [email protected]

Relative frequency in W

Relative frequency in D

(#of tuples in W that conatains x, y)/total # of tuples in W

(#of tuples in D that conatains x, y)/total # of tuples in D

Weimin He [email protected]

- Select * From D Where City=“Seattle” And View=“Waterfront”
- Y={SchoolDistrict, BoatDock, …}
- D=10,000 W=1000
- W{excellent}=10
- W{waterfront &yes}=5
- p(excellent|W)=10/1000=0.1
- p(excellent|D)=10/10,000=0.01
- p(waterfront|yes,W)=5/1000=0.005
- p(waterfront|yes,D)=5/10,000=0.0005

Weimin He [email protected]

{AttName, AttVal, Prob}

B+ tree index on (AttName, AttVal)

{AttName, AttVal, Prob}

B+ tree index on (AttName, AttVal)

{AttNameLeft, AttValLeft, AttNameRight, AttValRight, Prob}

B+ tree index on (AttNameLeft, AttValLeft, AttNameRight, AttValRight)

{AttNameLeft, AttValLeft, AttNameRight, AttValRight, Prob}

B+ tree index on (AttNameLeft, AttValLeft, AttNameRight, AttValRight)

Weimin He [email protected]

Preprocessing - Atomic Probabilities Module

- Computes and Indexes the Quantities P(y | W), P(y | D), P(x | y, W), and P(x | y, D) for All Distinct Values x and y
Execution

- Select Tuples that Satisfy the Query
- Scan and Compute Score for Each Result-Tuple
- Return Top-K Tuples

Weimin He [email protected]

- Scan algorithm is Inefficient
Many tuples in the answer set

- Another extreme
Pre-compute top-K tuples for all possible queries

Still infeasible in practice

- Trade-off solution
Pre-compute ranked lists of tuples for all possible atomic queries

At query time, merge ranked lists to get top-K tuples

Weimin He [email protected]

- CondList Cx
{AttName, AttVal, TID, CondScore}

B+ tree index on (AttName, AttVal, CondScore)

- GlobList Gx
{AttName, AttVal, TID, GlobScore}

B+ tree index on (AttName, AttVal, GlobScore)

Weimin He [email protected]

Weimin He [email protected]

Weimin He [email protected]

- Datasets:
- MSR HomeAdvisor Seattle (http://houseandhome.msn.com/)
- Internet Movie Database (http://www.imdb.com)

- Software and Hardware:
- Microsoft SQL Server2000 RDBMS
- P4 2.8-GHz PC, 1 GB RAM
- C#, Connected to RDBMS through DAO

Weimin He [email protected]

- Conducted on Seattle Homes and Movies tables
- Collect a workload from users
- Compare Conditional Ranking Method in the paper with the Global Method [CIDR03]

Weimin He [email protected]

- For each query Qi , generate a set Hi of 30 tuples likely to contain a good mix of relevant and irrelevant tuples
- Let each user mark 10 tuples in Hi as most relevant to Qi
- Measure how closely the 10 tuples marked by the user match the 10 tuples returned by each algorithm

Weimin He [email protected]

- 5 new queries
- Users were given the top-5 results

Weimin He [email protected]

- Datasets

- Compare 2 Algorithms:
- Scan algorithm
- List Merge algorithm

Weimin He [email protected]

Weimin He [email protected]

Weimin He [email protected]

Weimin He [email protected]

Weimin He [email protected]

- Automatic ranking for many-answers
- Adaptation of PIR to DB
- Mutiple-table query
- Non-categorical attributes

Weimin He [email protected]