This document discusses answering why-not questions for top-k queries. It begins with background on why-not questions and the history of explaining missing answers to queries. It then introduces the problem of answering why-not questions for top-k queries by explaining how to refine a top-k query to include a missing tuple in the results. The authors propose a sampling-based approach to find an optimal refined query with the minimum penalty by sampling weightings and stopping progress operations early. They present experiments on NBA data and synthetic data to evaluate their approach and optimization techniques.

1. Answering Why-not Questions
on Top-K Queries
Andy He and Eric Lo
The Hong Kong Polytechnic University

2. Background
 The database community has focused on
the performance issues for decades
 Recently more people turn their focus on
to the usability issues
 Supporting keyword search
 Query auto-completion
 Explaining your query result (a.k.a. Why and
Why-Not Questions)
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3. Why-Not Questions
 You post a query Q
 Database returns you a result R
 R gives you “surprise”
 E.g., a tuple m that you are expecting in the
result is missing, you ask “WHY??!”
 You pose a why-not question (Q,R,m)
 Database returns you an explanation E
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4. The (short) history of Why-Not
 Chapman and Jagadish
 “Why Not?” [SIGMOD 09]
 Select-Project-Join (SPJ) Questions
 Explanation E = “tell you which operator excludes
the expected tuple”
 Hung, Che, A.H. Doan, and J. Naughton
 “On the Provenance of Non-Answers to Queries
Over Extracted Data” [PVLDB 09]
 SPJ Queries
 Explanation E =“tell you how to modify the data”
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5. The (short) history of Why-Not
 Herschel and Herandez
 “Explaining Missing Answers to SPJUA Queries”
[PVLDB 10]
 SPJUA Queries
 Explanation E =“tell you how to modify the data”
 Tran and C.Y. Chan
 “How to Conquer why-not Questions” [SIGMOD
10]
 SPJA Queries
 Explanation E =“tell you how to modify your
query” 5/33

6. About this work
 Why-Not question on Top-k queries.
 Hotel <Price, Distance to CityCenter>
 Top-3 Hotel
 Weighting worigin =<0.5, 0.5>
 Result
 Rank 1: Sheraton
 Rank 2: Westin
 Rank 3: InterContinental
 “WHY my favorite Renaissance NOT in the Top-3 result?”
 If my value of k is too small?
 Or I should revise my weighting?
 Or need to modify both k and weighting?
 Explanation E = “tell you how to refine your Top-K query in
order to get your favorites back to the result”
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7. One possible answer
-only modify k
 Original query
Q(koriginal=3,woriginal=<0.5,0.5>)
 The ranking of Renaissance under the
original weighting woriginal=<0.5,0.5>
 Rank 1: Sheraton
 Rank 2: Westin
 Rank 3: InterContinental
 Rank 4: Hilton
 Rank 5: Renaissance
 Refined query #1: Q1(k=3,w=<0.5,0.5>)
5
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X

8. Another possible answer
-only modify weighting
 Original query Q(k=3,woriginal=<0.5,0.5>)
 Refined query #1: Q1(k=5,w=<0.5,0.5>)
 If we set weighting w=<0.1,0.9>
 Rank 1: Hotel E
 Rank 2: Hotel F
 Rank 3: Renaissance
 Refined query #2: Q2(k=3,w=<0.1,0.9>)
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9. Yet another possible answer
-modify both
 Original query Q(k=3,w=<0.5,0.5>)
 Refined query #1: Q1(k=5,w=<0.5,0.5>)
 Refined query #2: Q2(k=3,w=<0.1,0.9>)
 If we set weighting w=<0.9,0.1>
 Rank 1: Hotel A
 Rank 2: Hotel B
 Rank 3: Hotel C
 …
 …
 Rank 10000: Renaissance
 Refined query #3: Q3(k=10000,w=<0.9,0.1>)
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10. Our objective
 Find the refined query that minimizes a
penalty function with the missing tuple m
in the Top-K results
Prefer Modify K PMK
Prefer Modify Weighting PMW
Never Mind (Default) NM
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11. Basic idea
 For each weighting wi ∈ W
 Run PROGRESS(wi, UNTIL-SEE-m)
 Obtain the ranking ri of m under the weighting
wi
 Form a refined query Qi(k=ri,w=wi)
 Return the refined query with the least
penalty
W is
infinite!!!
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12. Our approach: sampling
 For each weighting wi ∈ W
 Run PROGRESS(wi, UNTIL-SEE-m)
 Obtain the ranking ri of m under the weighting
wi
 Form a refined query Qi(k=ri,w=wi)
 Return the refined query with the least
penalty
W is a set of
weightings draw from
a restricted weighting
space
Key Theorem: The optimal refined query
Qbest is either Q1 or else Qbest has a weighting
wbest in a restricted weighting space.
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W

13. How large the sample size should
be?
 We say a refined query is the best-T% refined
query if its penalty is smaller than (1-T)% refined
queries
 And we hope to get such a query with a
probability larger than a threshold Pr
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14. The PROGRESS operation can be
expensive
 Original query Q(k=3,woriginal=<0.5,0.5>)
 Refined query #1: Q1(k=5,w=<0.5,0.5>)
 If we set weighting w=<0.9,0.1>
 Rank 1: Hotel A
 Rank 2: Hotel B
 Rank 3: Hotel C
 …
 …
 Rank 10000: Renaissance
 Refined query: Q2(k=10000,w=<0.5,0.5>)
Very
Slow！！！
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15. Two optimization techniques
 Stop each PROGRESS operation early
 Skip some PROGRESS operations
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16. Stop earlier
 The original query Q(k=3,worigin=<0.5,0.5>)
 Refined query #1: Q1(k=5,w=<0.5,0.5>)
 If we set weighting w=<0.9,0.1>
 Rank 1: Hotel A
 Rank 2: Hotel B
 Rank 3: Hotel C
 …
 Rank 5: Hotel D
 …
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17. Skip PROGRESS operation(a)
 Similar weightings may lead to similar rankings
 Based on “Reverse Top-K” paper, ICDE’10
 Therefore
 The query result of PROGRESS(wx, UNTIL-SEE-m)
 could be used to deduce
 The query result of PROGRESS(wy, UNTIL-SEE-m)
 [Provided that wx and wy are similar]
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18. Skip PROGRESS operation(a)
 E.g., Original query Q(k=3,worigin=<0.5,0.5>)
 Refined query #1: Q1(k=5,w=<0.5,0.5>)
Score under w=<0.5,0.5>
Hotel Score
Sheraton 10
Westin 9
InterContinental 8
Hilton 7
Renaissance 6
Score under w=<0.6,0.4>
Hotel Score
Sheraton 9
Westin 10
InterContinental 7
Hilton 8
Renaissance 5
How the score
looks like if we
set w=<0.6,0.4>
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19. Skip PROGRESS operation(b)
 We can skip a weighting w if we find its
change ∆w between the original weighting
worigin is too large.
 E.g., We have a refined query with penalty
equals to 0.5, for a weighting w, if its changing
∆w is 1. We can totally skip it.
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20. Experiments
 Case Study on NBA data
 Experiments on Synthetic Data
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21. Case study on NBA data
 Compare with a pure random sampling
version
 Which do not draw sample from the restricted
weighting space but from the complete
weighting space
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22. Find the top-3 centers in NBA history
 5 Attributes (Weighting = 1/5)
 POINTS
 REBOUND
 BLOCKING
 FIELD GOAL
 FREE THROW
 Initial Result
 Rank 1: Chamberlain
 Rank 2: Abdul-Jabber
 Rank 3: O’Neal
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23. Find the top-3 centers in NBA history
Sampling on the
restricted sampling
space
Sampling on the
whole weighting
space
Refined query Top-3 Top-7
∆k 0 4
Time (ms) 156 154
Penalty 0.069 0.28
Why Not ?!
We choose “Prefer Modify Weighting”
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24. Synthetic Data
 Uniform, Anti-correlated, Correlated
 Scalability
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25. Varying query dimensions
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26. Varying ko
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27. Varying the ranking of the missing
object
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28. Varying the number of missing
objects
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29. Varying T%
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Time Time
Quality Quality

30. Varying Pr
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31. Optimization effectiveness
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32. Conclusions
 We are the first one to answer why-not question on top-k
query
 We prove that finding the optimal answer is
computationally expensive
 A sampling based method is proposed
 The optimal answer is proved to be in a restricted
sample space
 Two optimization techniques are proposed
 Stop each PROGRESS operation early
 Skip some PROGRESS operations
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33. Thanks
Q&A

34. Deal with multiple missing objects M
 We have to modify the algorithm a litte bit:
 Do a simple filtering on the set of missing
objects
 If mi dominates mj in the data space
 Remove mi from M Because every time mj shows
up in a top-k result, mi must be there
 Condition UNTIL-SEE-m becomes UNTIL-
SEE-ALL-OBJECTS-IN-M
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35. Penalty Model
 Original Query Q(3, worigin)
 Refined Query Q1(5, worigin)
 Penalty of changing k
 ∆ k = 5 - 3 = 2
 Penalty of changing w
 ∆ w = ||worigin -worigin||2=0
 Basic penalty model
 Penalty(5,w0) = λk ∆ k + λw ∆ w
 (λk + λw = 1)
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36. Normalized penalty function
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