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1
Efficient Computation of Diverse Query Results
Erik Vee
joint work with
Utkarsh Srivastava, Jayavel Shanmugasundaram,Prashant Bhat, Sihem Amer Yahia
Talk modified for CS 632 by S. Sudarshan
2
Motivation
• Imagine looking for shoes on Yahoo! Shopping, and seeing only Reeboks
3
Motivation
• Imagine looking for shoes on Yahoo! Shopping, and seeing only Reeboks
• … or looking for cars on Yahoo! Autos, andseeing only Hondas
4
Motivation
• Imagine looking for shoes on Yahoo! Shopping, and seeing only Reeboks
• … or looking for cars on Yahoo! Autos, andseeing only Hondas
• … or looking for jobs on Yahoo! Hotjobs, andseeing only jobs from Yahoo!
• It is not enough to simply give the best response– Need diversity of answers
5
Diversity Search
• If we display 30 results in 5 categories, then should show 6 items from each category– NB: Our goal is to show range of choices,
not representative sample
– Recurse on each subgroup of items
• Diversity crucial for users looking for range of results– e.g. Shopping, information gathering/research
• Useful for aiding navigation– Users tend to favor search-and-click over hierarchies
• Likely to give at least one good answer on first page
6
Contributions
• Formally define diversity search– Other diversity-like approaches use extensive post-processing
or are not query-dependent
• Proved that traditional IR engines cannot produce guaranteed diverse results
• Gave novel algorithms to produce diverse results– Both one-pass (datastreaming) and probing algorithms
• Experimentally verified that these results are nearly as fast as normal top-k processing– Much faster than post-processing techniques
7
What about other approaches?
• If not diverse enough, query again– E.g. If all results are from one company, issue another query– Bad for latency
• Issue multiple queries (one for Honda, one for Toyota...)– Can be prohibitively expensive (kills throughput)
• latency fine
– Some applications may have dozens of top-level categories
• Fetch extra results, then find most diverse set from this– Not guaranteed to get good results– Requires fetching additional results unnecessarily
• Fetch all results, then find diverse set– Many times slower
• Random sample of results– Miss important results this way
8
What about clever scoring?
• Can we give each item a global “diversity” score, then find top-k using this?– Prove in paper: There is no global score that gives guaranteed
diversity
• Can we give each item a local “diversity” score, so that it has a different score in each list of the inverted index?– Prove in paper: There is no list-based scoring of the item that
gives guaranteed diversity
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Outline
• Definition of diversity
• Overview of our algorithms
• Our experimental results
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Diversity search
• Over all possible sets of top-k results that match query, return set with most diversity
• Paper defines diversity more precisely– Focus on hierarchy view of diversity (in next slides)
• For scored diversity (in which each item has a score)– Over all possible sets of top-k results with maximum score,
return set with highest diversity
– Note: Diversity only useful when score not too fine-grained
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Diversity definition (by picture)
Implicitly defineshierarchy
Make
Model
Color
Year
Text
Determine a category ordering
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Hierarchy after a query
Diversity search alwaysreturns valid results
E.g. Query text contains `Low`
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Hierarchy after a query
Diversity search alwaysreturns valid results
E.g. Query text contains `Low`
All siblings return thesame number of results(or as close as possible)
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Returning top-k diverse results
Diversity search alwaysreturns valid results
E.g. Query text contains `Low`
Suppose return k=4 results
Must return 2 Hondas and 2 ToyotasWill not
return2 green Civics
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Outline
• Definition of diversity
• Overview of our algorithms
• Our experimental results
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Algorithms
• One Pass– Never goes backward (just one pass over dataset)
– Maintains a top-k diverse set based on what has been seen
– Jumps ahead if more results will not help diversity
– Optimal one-pass algorithm
• Probe– May jump forward or backward (i.e. probes)
– Prove: at most 2k probes for top-k diverse result set
• Both also work for scored diversity
17
Dewey IDs
Every branch gets a number
Every item then labeled,e.g. 0.2.0.1.0 isHonda Odyssey Green ’06 `Good miles’
Create invertedindex
low 00000, 00010, 00100, 00200, 00300, 00310, 10000, 11000, 12000, 13000
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Next and Prev
Supports two basic operations: Next and Prev
E.g. Query text contains `Low`
Next(0.0.3.2.2) = 1.0.0.0.0Prev(2.0.0.0.0) = 1.3.0.0.0
Inverted index for ‘Low’ listsall items in Dewey ID order
In general, must find intersection of lists (still easy)
low 00000, 00010, 00100, 00200, 00300, 00310, 10000, 11000, 12000, 13000
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One pass (for k = 2)
First finds 00000, 00010
Now knows Civic Greenno longer helps
Jumps by callingnext(0.0.1.0.0)
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Finds 00100Removes 00010
One pass (for k = 2)
First finds 00000, 00010
Now knows Civic Greenno longer helps!
Jumps by callingnext(0.0.1.0.0)
Now knows Civicno longer helps!
Jumps by callingnext(0.1.0.0.0)
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Finds 00100Removes 00010
One pass (for k = 2)
First finds 00000, 00010
Now knows Civic Greenno longer helps!
Jumps by callingnext(0.0.1.0.0)
Now knows Civicno longer helps!
Jumps by callingnext(0.1.0.0.0)
Finds 01000Removes 00100 Knows to stop
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Unscored One-Pass Algorithm
Key step: deciding where to skip to
Remove 1st element in queue
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One-Pass Algorithm (Cont.)
• Complexity: k lnd(3k)
• Scored One Pass Algo: same algo as for unscored case, except:– replace line 11 of the unscored one-pass algorithm with the line
• id = mergedList.next(id+1, skipId, root, minScore)
• The semantics of the above line is to return the smallest id greater than or equal to id+1 such that either
– score(id) > root.minScore, or
– score(id) >= root.minScore, and the return id is greater than skipId.
24
Probe (for k = 4)
Calls next(0.0.0.0.0) and prev(. . . . )to find first and last items
Wants another Honda
Calls prev(0. . . . )
Discovers there are only2 top-level categories
25
Probe (for k = 4)
Calls next(0.0.0.0.0) and prev(. . . . )to find first and last items
Wants another Honda
Calls prev(0. . . . )
Why not next(0.1.0.0.0)?
If Honda has only onechild, then will returna Toyota!
26
Probe (for k = 4)
Calls next(0.0.0.0.0) and prev(. . . . )to find first and last items
Wants another Honda
Calls prev(0. . . . )
Finds 00310
Wants another Toyota
Calls next(1.0.0.0.0)
27
Probe (for k = 4)
Calls next(0.0.0.0.0) and prev(. . . . )to find first and last items
Wants another Honda
Calls prev(0. . . . )
Finds 00310
Wants another Toyota
Calls next(1.0.0.0.0)
Finds 10000
28
Unscored Probing Algorithm
29
Unscored Probing (Cont.)
30
Unscored Probing (Cont.)
31
Unscored Probing (Cont.)
32
Unscored Probing
• Invariant: Whenever id node, either id belongs to some child of node in our data structure, or node.edge[LEFT] <= id <= node.edge[RIGHT]
• Invariant: Let node be some node in our data structure, and suppose during the execution of the algorithm, we call node.getProbeId(), returning (probeId, dir). Then we have mergedList.next(probeId, dir) node.
• Theorem 2: The unscored probing algorithm given in Algorithms 2, 3 makes at most 2k calls to next.
33
Scored Probing (Cont.)
• Let be the score of the lowest-scoring item in thetop-K list returned. Diversity is only guaranteed among items whose score is . – The difficulty comes from not knowing the exact value of .
34
Scored Probing
35
Outline
• Definition of diversity
• Overview of our algorithms
• Our experimental results
36
Results
• Dataset consisted of listing from Yahoo! Autos
• Queries were synthetic to test various parameters– Selectivity, # predicates, # results
• Preprocessing time for 100K listings < 5min– Times shown are for 5K queries
• 4 algorithms– Basic: No diversity
– Naïve: Fetch everything, post-process
– OnePass: Our algorithm. Takes just one pass over data
– Probe: Our algorithm. May make multiple probes into data
37
Comparable time for diversity search
unscored scored
Basic: No diversity
Naïve: Many times slower OnePass: Close to probe
Probe: Within factor 2 of no diversity
MultiQuery (not shown): Latency close to Basic, but throughput many times worse
38
Results summary
• Getting diverse results not too much slower than getting non-diverse results– Many times faster than naïve approaches
• Multi-query approach has even worse throughput than naïve– But keeps latency low
• How does this compare to getting extra results, then finding a diverse subset?– Getting 2k results instead of k is about twice as slow
– Plus, does not guarantee diverse results
39
Conclusions
• Can get guaranteed diversity, taking time close to normal top-k query– Almost as fast or faster than non-guaranteed results
– Diversity at every level
• Works even when items have scores
• Needs a different algorithm than traditional IR engines– Proved this in paper (under standard notions)
• Are there approximate notions that can use existing IR machinery?
40