Efficient Computation of Diverse Query Results

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

9. Outline • Definition of diversity • Overview of our algorithms • Our experimental results

10. 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

11. Diversity definition (by picture) Determine a category ordering Make Implicitly defines hierarchy Model Color Year Text

12. Hierarchy after a query Diversity search always returns valid results E.g. Querytext contains `Low`

13. Hierarchy after a query All siblings return the same number of results (or as close as possible) Diversity search always returns valid results E.g. Querytext contains `Low`

14. Returning top-k diverse results Diversity search always returns valid results E.g. Querytext contains `Low` Suppose return k=4 results Must return 2 Hondas and 2 Toyotas Will not return2 green Civics

15. Outline • Definition of diversity • Overview of our algorithms • Our experimental results

16. 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 is Honda Odyssey Green ’06 `Good miles’ Create inverted index low  00000, 00010, 00100, 00200, 00300, 00310, 10000, 11000, 12000, 13000

18. Next and Prev Supports two basic operations: Next and Prev E.g. Querytext contains `Low` Next(0.0.3.2.2) = 1.0.0.0.0 Prev(2.0.0.0.0) = 1.3.0.0.0 Inverted index for ‘Low’ lists all 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

19. One pass (for k = 2) First finds 00000, 00010 Now knows Civic Green no longer helps Jumps by calling next(0.0.1.0.0)

20. One pass (for k = 2) First finds 00000, 00010 Now knows Civic Green no longer helps! Jumps by calling next(0.0.1.0.0) Finds 00100 Removes 00010 Now knows Civic no longer helps! Jumps by calling next(0.1.0.0.0)

21. One pass (for k = 2) First finds 00000, 00010 Now knows Civic Green no longer helps! Jumps by calling next(0.0.1.0.0) Finds 00100 Removes 00010 Now knows Civic no longer helps! Jumps by calling next(0.1.0.0.0) Finds 01000 Removes 00100 Knows to stop

22. Unscored One-Pass Algorithm Remove 1st element in queue Key step: deciding where to skip to

23. 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) Discovers there are only 2 top-level categories Calls next(0.0.0.0.0) and prev(. . . . ) to find first and last items Wants another Honda Calls prev(0. . . . )

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 one child, then will return a 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 Probe: Within factor 2 of no diversity Basic: No diversity Naïve: Many times slower OnePass: Close to probe 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?