1. 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

2. Outline Motivation Problem Definition System Architecture
Construction of Ranking Function
Implementation
Experiments
Conclusion and open problems
11/21/2018
Weimin He

3. Motivating example 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
11/21/2018
Weimin He

4. Motivation Many-answers problem Two alternative solutions:
Query reformulation
Automatic ranking
Apply probabilistic model in IR to DB tuple ranking
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Weimin He

5. Problem Definition
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 ?
11/21/2018
Weimin He

6. System Architecture
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Weimin He

7. Intuition for Ranking Function
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
11/21/2018
Weimin He

8. Probabilistic Model in IR
Bayes’ Rule
Product Rule
Document t, Query Q R: Relevant document set R = D - R: Irrelevant document set
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Weimin He

9. Adaptation of PIR to DB 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
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Weimin He

10. Preliminary Derivation
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Weimin He

11. Limited Independence Assumptions
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
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Weimin He

12. Continuing Derivation
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Weimin He

13. Workload-based Estimation of
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
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Weimin He

14. Final Ranking Function
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Weimin He

15. Pre-computing Atomic Probabilities in Ranking Function
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
11/21/2018
Weimin He

16. Example for Computing Atomic Probabilities
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
11/21/2018
Weimin He

17. Indexing Atomic Probabilities
{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)
11/21/2018
Weimin He

18. Scan Algorithm 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
11/21/2018
Weimin He

19. Beyond Scan Algorithm 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
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Weimin He

20. Two kinds of Ranked List
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)
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Weimin He

21. Index Module
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Weimin He

22. List Merge Algorithm
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Weimin He

23. Experimental Setup Datasets:
MSR HomeAdvisor Seattle (
Internet Movie Database (
Software and Hardware:
Microsoft SQL Server2000 RDBMS
P4 2.8-GHz PC, 1 GB RAM
C#, Connected to RDBMS through DAO
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Weimin He

24. Quality Experiments Conducted on Seattle Homes and Movies tables
Collect a workload from users
Compare Conditional Ranking Method in the paper with the Global Method [CIDR03]
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Weimin He

25. Quality Experiment-Average Precision
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
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Weimin He

26. Quality Experiment- Fraction of Users Preferring Each Algorithm
5 new queries
Users were given the top-5 results
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Weimin He

27. Performance Experiments
Datasets
Compare 2 Algorithms:
Scan algorithm
List Merge algorithm
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Weimin He

28. Performance Experiments – Pre-computation Time
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Weimin He

29. Performance Experiments – Execution Time
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Weimin He

30. Performance Experiments – Execution Time
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Weimin He

31. Performance Experiments – Execution Time
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Weimin He

32. Conclusion and Open Problems
Automatic ranking for many-answers
Adaptation of PIR to DB
Mutiple-table query
Non-categorical attributes
11/21/2018
Weimin He