1 Efficient Computation of Diverse Query Results Erik Vee joint work with Utkarsh Srivastava,...

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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

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Motivation

• Imagine looking for shoes on Yahoo! Shopping, and seeing only Reeboks

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Motivation

• Imagine looking for shoes on Yahoo! Shopping, and seeing only Reeboks

• … or looking for cars on Yahoo! Autos, andseeing only Hondas

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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

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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

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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

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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

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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

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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.

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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

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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!

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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)

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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

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Unscored Probing Algorithm

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Unscored Probing (Cont.)

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Unscored Probing (Cont.)

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Unscored Probing (Cont.)

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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.

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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 .

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Scored Probing

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Outline

• Definition of diversity

• Overview of our algorithms

• Our experimental results

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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

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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

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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

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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?

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