Advanced Search Techniques for Large Scale Data Analytics
Pavel Zezula and Jan Sedmidubsky
Masaryk University
http://disa.fi.muni.cz

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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)





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a
b
c
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Boys
Girls
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
Nodes: Boys and Girls; Edges: Preferences
Goal: Match boys to girls so that maximum
number of preferences is satisfied

M = {(1,a),(2,b),(3,d)} is a matching
Cardinality of matching = |M| = 3
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Boys
Girls
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)

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b
c
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Boys
Girls
M = {(1,c),(2,b),(3,d),(4,a)} is a
perfect matching
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
Perfect matching … all vertices of the graph are matched
Maximum matching …  a matching that contains the largest possible number of matches

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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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1
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a
b
c
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(1,a)
(2,b)
(3,d)

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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


¡For input I, suppose greedy produces matching Mgreedy while an optimal
matching is Mopt
¡
¡Competitive ratio =
¡ minall possible inputs I (|Mgreedy|/|Mopt|)
¡
¡(what is greedy’s worst performance over all possible inputs I)
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)

¡Consider a case: Mgreedy≠ Mopt
¡Consider the set G of girls
matched in Mopt but not in Mgreedy
¡Then every boy B adjacent to girls
in G is already matched in Mgreedy:
§If there would exist such non-matched
(by Mgreedy) boy adjacent to a non-matched
girl then greedy would have matched them
¡Since boys B are already matched in Mgreedy then
(1) |Mgreedy|≥ |B|
¡
Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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a
b
c
d
G={     }
B={          }
Mopt
1
2
3
4

¡Summary so far:
§Girls G matched in Mopt but not in Mgreedy
§(1) |Mgreedy|≥ |B|
¡There are at least |G| such boys
(|G| £ |B|) otherwise the optimal
algorithm couldn’t have matched all girls in G
§So: |G| £ |B| £ |Mgreedy|
¡By definition of G also: |Mopt| £ |Mgreedy| + |G|
§Worst case is when |G| = |B| = |Mgreedy|
¡|Mopt| £ 2|Mgreedy| then |Mgreedy|/|Mopt| ³ 1/2
¡
¡
Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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a
b
c
d
G={     }
B={          }
Mopt
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2
3
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This is a general proof.
We make no assumptions about the structure of the bipartite graph.

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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)




¡Banner ads (1995-2001)
§Initial form of web advertising
§Popular websites charged
X$ for every 1,000
“impressions” of the ad
§Called “CPM” rate
(Cost per thousand impressions)
§Modeled similar to TV, magazine ads
§From untargeted to demographically targeted
§Low click-through rates
§Low ROI for advertisers
Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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CPM…cost per mille
Mille…thousand in Latin

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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


google-results google-ads
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)

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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


¡Given:
§1. A set of bids by advertisers for search queries
§2. A click-through rate for each advertiser-query pair
§3. A budget for each advertiser (say for 1 month)
§4. A limit on the number of ads to be displayed with each search query
¡Respond to each search query with a set of advertisers such that:
§1. The size of the set is no larger than the limit on the number of ads per query
§2. Each advertiser has bid on the search query
§3. Each advertiser has enough budget left to pay for the ad if it is clicked upon
Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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Advertiser
Bid
CTR
Bid * CTR
A
B
C
$1.00
$0.75
$0.50
1%
2%
2.5%
1 cent
1.5 cents
1.125 cents
Click through
rate
Expected
revenue

¡Two complications:
§Budget
§CTR of an ad is unknown
¡
¡Each advertiser has a limited budget
§Search engine guarantees that the advertiser
will not be charged more than their daily budget
Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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¡CTR: Each ad has a different likelihood of being clicked
§Advertiser 1 bids $2, click probability = 0.1
§Advertiser 2 bids $1, click probability = 0.5
§Clickthrough rate (CTR) is measured historically
§Very hard problem: Exploration vs. exploitation
Exploit: Should we keep showing an ad for which we have
good estimates of click-through rate
or
Explore:  Shall we show a brand new ad to get a better sense of its click-through rate
Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


¡Two advertisers A and B
§A bids on query x, B bids on x and y
§Both have budgets of $4
¡Query stream: x x x x y y y y
§Worst case greedy choice: B B B B _ _ _ _
§Optimal:  A A A A B B B B
§Competitive ratio = ½
¡This is the worst case!
§Note: Greedy algorithm is deterministic – it always
resolves draws in the same way
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)

Is greedy deterministic or randomized (it is deterministic!!)

¡BALANCE Algorithm by Mehta, Saberi, Vazirani, and Vazirani
§For each query, pick the advertiser with the
largest unspent budget
§Break ties arbitrarily (but in a deterministic way)
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)

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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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Why exhausts budget:
-- remember, optimal exhausts both budgets
GENERAL PROOF

A1
A2
B
x
y
B
A1
A2
x
Optimal revenue = 2B
Assume Balance gives revenue = 2B-x = B+y
Queries allocated to A1 in the optimal solution
Queries allocated to A2 in the optimal solution
Not
used
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
BALANCE exhausts A2’s budget
x
y
B
A1
A2
x
Not
used

Whatever is not used should be assigned to A2 (since if we could assign to A1 we would since we
still have the budget)
CASE 1) Less than half of A1’s queries got assigned to A2. So y>B/2
CASE 2) If more than half of A1’s queries got assigned to A2.
Consider last of A1s queries assigned to A2. At that time B2 > B1.
At that time B2 < ½. Since more than half of A1’s queries got assigned to A2 (this means the
remaining budget had to be <1/2).
So B1<1/2.

¡In the general case with N advertisers, worst competitive ratio of BALANCE is 1–1/e = approx. 0.63
§Interestingly, no online algorithm has a better competitive ratio!
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)




¡Customer X
§Buys Metallica CD
§Buys Megadeth CD
¡Customer Y
§Does search on Metallica
§Recommender system suggests Megadeth from data collected about customer X
classic alive
Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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http://blog.hubspot.com/Portals/249/images/amazon_logo.gif
http://4.bp.blogspot.com/_zmoEeqomXD4/SjftFPB6UTI/AAAAAAAACZE/gxQm5CcUp_k/s400/del.icio.us-logo.jpg
http://upload.moldova.org/IT/logos/youtube_logo.gif
Items
MCBS01705_0000[1]
Search
Recommendations
Products, web sites,
blogs, news items, …
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
Pandora Logo http://scrapetv.com/News/News%20Pages/Business/images-5/netflix-logo.jpg
http://www.growyourwritingbusiness.com/images/stumbleupon_logo.bmp
http://admintell.napco.com/ee/images/uploads/appletell/618px-Last.fm_logo_.svg_.png
Examples:
http://upload.wikimedia.org/wikipedia/commons/5/52/Movielens-helping.gif
http://blog.ithenticate.com/wp-content/uploads/2010/11/google-news-logo.png
http://beefjack.com/files/2010/04/xbox-live-arcade.thumbnail.jpg

Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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In 1988, a British mountain climber named Joe Simpson wrote a book called Touching the Void, a
harrowing account of near death in the Peruvian Andes. It got good reviews but, only a modest
success, it was soon forgotten. Then, a decade later, a strange thing happened. Jon Krakauer
wroteInto Thin Air, another book about a mountain-climbing tragedy, which became a publishing
sensation. SuddenlyTouching the Void started to sell again.
Random House rushed out a new edition to keep up with demand. Booksellers began to promote it next
to their Into Thin Air displays, and sales rose further. A revised paperback edition, which came
out in January, spent 14 weeks on theNew York Times bestseller list. That same month, IFC Films
released a docudrama of the story to critical acclaim. NowTouching the Void outsells Into Thin
Air more than two to one.
What happened? In short, Amazon.com recommendations. The online bookseller's software noted
patterns in buying behavior and suggested that readers who liked Into Thin Airwould also
like Touching the Void. People took the suggestion, agreed wholeheartedly, wrote rhapsodic reviews.
More sales, more algorithm-fueled recommendations, and the positive feedback loop kicked in.

Anatomy edit
Source: Chris Anderson (2004)
Full-size image
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


Avatar
LOTR
Matrix
Pirates
Alice
Bob
Carol
David
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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)

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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)


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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)

Latent factor based – predict recommendations that the user has not seen yet by building a system
working well on known ratings and hope it predicts unknown ratings also well




¡Main idea: Recommend items to customer x similar to previous items rated highly by x
¡
¡Example:
¡Movie recommendations
§Recommend movies with same actor(s),
director, genre, …
¡Websites, blogs, news
§Recommend other sites with “similar” content
§
Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
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MCBS01705_0000[1]
likes
Item profiles
Red
Circles
Triangles
User profile
match
recommend
build
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J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org

Item profile = vector of item features (e.g., one dimension = 0/1 whether it is red color, or not)
User profile = e.g., average over item profiles

J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org
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Harnessing quality judgments of other users



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Pavel Zezula, Jan Sedmidubsky. Advanced Search Techniques for Large Scale Data Analytics (PA212)
Figure
x
N