Presentation by J. Tipan Verella from Millennial Media at the Insight Summit Series: 2014 Digital Advertising + Marketing Summit

1. Graph Theory for Online Advertising
J. Tipan Verella
March 19, 2014
Tipan GTOA March 19, 2014 1 / 18

2. Introduction
What is so great about Graphs?
A Graph
G = (V ;E) is a pair of sets, vertices and edges.
Tipan GTOA March 19, 2014 2 / 18

3. Introduction
What is so great about Graphs?
A Graph
G = (V ;E) is a pair of sets, vertices and edges.
Degree of Vertex, Connected Components
Tipan GTOA March 19, 2014 2 / 18

4. Introduction
What is so great about Graphs?
A Graph
G = (V ;E) is a pair of sets, vertices and edges.
Degree of Vertex, Connected Components
Systems
Engineering for Complex Behavioral Systems
bio-chemical reaction networks,
ecological systems, distributed adaptive
systems; self-organization, phase transition
markets,
herd behavior and crowdsourcing, bittorrent
Tipan GTOA March 19, 2014 2 / 18

5. Introduction
What is so great about Graphs?
A Graph
G = (V ;E) is a pair of sets, vertices and edges.
Degree of Vertex, Connected Components
Systems
Engineering for Complex Behavioral Systems
bio-chemical reaction networks,
ecological systems, distributed adaptive
systems; self-organization, phase transition
markets,
herd behavior and crowdsourcing, bittorrent
Graphs (Networks) are a versatile tool for
understanding structures of Complex Systems.
Tipan GTOA March 19, 2014 2 / 18

6. Introduction
What is so great about Graphs?
A Graph
G = (V ;E) is a pair of sets, vertices and edges.
Degree of Vertex, Connected Components
Systems
Engineering for Complex Behavioral Systems
bio-chemical reaction networks,
ecological systems, distributed adaptive
systems; self-organization, phase transition
markets,
herd behavior and crowdsourcing, bittorrent
Graphs (Networks) are a versatile tool for
understanding structures of Complex Systems.
What does it have to do with online advertising?
Tipan GTOA March 19, 2014 2 / 18

7. Introduction
Anecdotes from the Industry
1
https://www.facebook.com/notes/facebook-engineering/scaling-apache-giraph-to-
a-trillion-edges/10151617006153920
2
http://research.microsoft.com/en-us/projects/ldg/
3
https://giraph.apache.org/
4
http://dl.acm.org/citation.cfm?id=1807184
Tipan GTOA March 19, 2014 3 / 18

8. Introduction
Anecdotes from the Industry
Facebook Presto 2013, Demonstrating the Scalability of Presto1
1
https://www.facebook.com/notes/facebook-engineering/scaling-apache-giraph-to-
a-trillion-edges/10151617006153920
2
http://research.microsoft.com/en-us/projects/ldg/
3
https://giraph.apache.org/
4
http://dl.acm.org/citation.cfm?id=1807184
Tipan GTOA March 19, 2014 3 / 18

9. Introduction
Anecdotes from the Industry
Facebook Presto 2013, Demonstrating the Scalability of Presto1
Microsoft Horton (2012) is a research project in the eXtreme
Computing Group to enable querying large distributed
graphs.2
1
https://www.facebook.com/notes/facebook-engineering/scaling-apache-giraph-to-
a-trillion-edges/10151617006153920
2
http://research.microsoft.com/en-us/projects/ldg/
3
https://giraph.apache.org/
4
http://dl.acm.org/citation.cfm?id=1807184
Tipan GTOA March 19, 2014 3 / 18

10. Introduction
Anecdotes from the Industry
Facebook Presto 2013, Demonstrating the Scalability of Presto1
Microsoft Horton (2012) is a research project in the eXtreme
Computing Group to enable querying large distributed
graphs.2
Yahoo! Apache Giraph (2011) is an iterative graph processing
system built for high scalability.3
1
https://www.facebook.com/notes/facebook-engineering/scaling-apache-giraph-to-
a-trillion-edges/10151617006153920
2
http://research.microsoft.com/en-us/projects/ldg/
3
https://giraph.apache.org/
4
http://dl.acm.org/citation.cfm?id=1807184
Tipan GTOA March 19, 2014 3 / 18

11. Introduction
Anecdotes from the Industry
Facebook Presto 2013, Demonstrating the Scalability of Presto1
Microsoft Horton (2012) is a research project in the eXtreme
Computing Group to enable querying large distributed
graphs.2
Yahoo! Apache Giraph (2011) is an iterative graph processing
system built for high scalability.3
Google Pregel (2010) A System for Large-Scale Graph Processing4
Inspired by Leslie Valiant’s Bulk Synchronous Parallel model for distributed
computing.
1
https://www.facebook.com/notes/facebook-engineering/scaling-apache-giraph-to-
a-trillion-edges/10151617006153920
2
http://research.microsoft.com/en-us/projects/ldg/
3
https://giraph.apache.org/
4
http://dl.acm.org/citation.cfm?id=1807184
Tipan GTOA March 19, 2014 3 / 18

12. Strategy and Structure Optimization Problems in Online Performance Advertising
Performance Advertising
Advertiser would prefer to only pay for actions
Publisher would prefer to only charge on views (impressions)
Tipan GTOA March 19, 2014 4 / 18

13. Strategy and Structure Optimization Problems in Online Performance Advertising
The Advertiser Problem
j is the proportion of your budget you spend on site j
Nj (
j ) are the impressions procured by spending
j on site j
j is the conversion rate of your ad on site j
Tipan GTOA March 19, 2014 5 / 18

14. Strategy and Structure Optimization Problems in Online Performance Advertising
The Advertiser Problem
j is the proportion of your budget you spend on site j
Nj (
j ) are the impressions procured by spending
j on site j
j is the conversion rate of your ad on site j
max
j2J
Nj (
j ) ¡ j
Actionsj
subject to:
j
j Budget
Tipan GTOA March 19, 2014 5 / 18

15. Strategy and Structure Optimization Problems in Online Performance Advertising
The Publisher Problem
(i;n) is the revenue if impression n is awarded to advertiser i

16. i;n is 1 or 0 depending on whether or not impression n is
awarded to advertiser i
I is the set of advertisers
Tipan GTOA March 19, 2014 6 / 18

17. Strategy and Structure Optimization Problems in Online Performance Advertising
The Publisher Problem
(i;n) is the revenue if impression n is awarded to advertiser i

18. i;n is 1 or 0 depending on whether or not impression n is
awarded to advertiser i
I is the set of advertisers
max

19. i;n
n2N i2I
(i;n) ¡

20. i;n
subject to:
i2I

21. i;n 1 Vn
Tipan GTOA March 19, 2014 6 / 18

22. Strategy and Structure Optimization Problems in Online Performance Advertising
The AdNetwork Problem
i;j is the fraction of the inventory on site j allocated to
advertiser i
Nj are the total number of impressions from site j
i;j is the conversion rate of advertiser i on site j
(i) is the amount paid per conversion by advertiser i
cj is the cost per impression on site j
Bi is the budget of advertiser i
Tipan GTOA March 19, 2014 7 / 18

23. Strategy and Structure Optimization Problems in Online Performance Advertising
The AdNetwork Problem
i;j is the fraction of the inventory on site j allocated to
advertiser i
Nj are the total number of impressions from site j
i;j is the conversion rate of advertiser i on site j
(i) is the amount paid per conversion by advertiser i
cj is the cost per impression on site j
Bi is the budget of advertiser i
max
i2I j2J
0
B@i;j ¡ Nj ¡ i;j ¡ (i)
revenue
−
cost
cj ¡ Nj
1
CA
subject to:
j2J
i;j ¡ Nj ¡ i;j ¡ (i) Bi Vi P I
i2I
i;j 1 Vj P J
Tipan GTOA March 19, 2014 7 / 18

24. Strategy and Structure Optimization Problems in Online Performance Advertising
The Centralized Approach: Linear Programming
max
i2I j2J
0
B@i;j ¡ Nj ¡ i;j ¡ (i)
revenue
−
cost
cj ¡ Nj
1
CA
subject to:
j2J
i;j ¡ Nj ¡ i;j ¡ (i)
spend of advertiser i
Bi Vi P I
i2I
i;j 1 Vj P J
Plan, Evaluate, Update
Duality can says a lot about the structure of your problem
Tipan GTOA March 19, 2014 8 / 18

25. Strategy and Structure Optimization Problems in Online Performance Advertising
The Centralized Approach: Linear Programming
max
i2I j2J
0
B@i;j ¡ Nj ¡ i;j ¡ (i)
revenue
−
cost
cj ¡ Nj
1
CA
subject to:
j2J
i;j ¡ Nj ¡ i;j ¡ (i)
spend of advertiser i
Bi Vi P I
i2I
i;j 1 Vj P J
Plan, Evaluate, Update
Duality can says a lot about the structure of your problem
DOES NOT SCALE!
Tipan GTOA March 19, 2014 8 / 18

26. Strategy and Structure Optimization Problems in Online Performance Advertising
The Decentralized Approach: The Market Paradigm
Publisher runs auctions, the good (impressions) goes to the agent
that values it the most 5
the monopoly should provide as detailed a description of
the good as possible
the auction solves the allocation problem
Advertiser places bids, 2nd price auction it is optimal to bid your
valuation
valuation depends on conversion rates, a priori unknown!
the number of auctions is also unknown!
5
Hal Varian on the Online Ad Auction
Tipan GTOA March 19, 2014 9 / 18

27. Strategy and Structure Optimization Problems in Online Performance Advertising
The Decentralized Approach: The Market Paradigm
Publisher runs auctions, the good (impressions) goes to the agent
that values it the most 5
the monopoly should provide as detailed a description of
the good as possible
the auction solves the allocation problem
Advertiser places bids, 2nd price auction it is optimal to bid your
valuation
valuation depends on conversion rates, a priori unknown!
the number of auctions is also unknown!
performance rates have to be estimated
control algorithms have to be implemented in order to
pace the delivery of the ad campaign
5
Hal Varian on the Online Ad Auction
Tipan GTOA March 19, 2014 9 / 18

28. Strategy and Structure Optimization Problems in Online Performance Advertising
The Decentralized Approach: The Market Paradigm
Publisher runs auctions, the good (impressions) goes to the agent
that values it the most 5
the monopoly should provide as detailed a description of
the good as possible
the auction solves the allocation problem
Advertiser places bids, 2nd price auction it is optimal to bid your
valuation
valuation depends on conversion rates, a priori unknown!
the number of auctions is also unknown!
performance rates have to be estimated
control algorithms have to be implemented in order to
pace the delivery of the ad campaign
Markets are complex systems!
5
Hal Varian on the Online Ad Auction
Tipan GTOA March 19, 2014 9 / 18

29. Strategy and Structure Graphs and Behavior
More About Graphs: Random Graphs
Let V be a vertex set, with |V | = n.
For each pair of vertices (u;v), with u;v P V , we decide to put the
edge (u;v) based on the outcome of a coin flip, with probability
p = c
n .
Tipan GTOA March 19, 2014 10 / 18

30. Strategy and Structure Graphs and Behavior
Erd¨os and R´enyi
Paul Erd¨os and Alfred R´enyi6 proved (1960) that such a graph experience
a phase transition at c = 1.
6
On the Evolution of Random Graphs
Tipan GTOA March 19, 2014 11 / 18

31. Strategy and Structure Graphs and Behavior
Erd¨os and R´enyi
Paul Erd¨os and Alfred R´enyi6 proved (1960) that such a graph experience
a phase transition at c = 1.
Figure : as c goes from 1 to 1
6
On the Evolution of Random Graphs
Tipan GTOA March 19, 2014 11 / 18

32. Strategy and Structure Graphs and Behavior
Erd¨os and R´enyi
Paul Erd¨os and Alfred R´enyi6 proved (1960) that such a graph experience
a phase transition at c = 1.
Figure : as c goes from 1 to 1
6
On the Evolution of Random Graphs
Tipan GTOA March 19, 2014 11 / 18

33. Strategy and Structure Graphs and Behavior
Erd¨os and R´enyi
Paul Erd¨os and Alfred R´enyi6 proved (1960) that such a graph experience
a phase transition at c = 1.
Figure : as c goes from 1 to 1
6
On the Evolution of Random Graphs
Tipan GTOA March 19, 2014 11 / 18

34. Strategy and Structure Graphs and Behavior
Erd¨os and R´enyi
Paul Erd¨os and Alfred R´enyi6 proved (1960) that such a graph experience
a phase transition at c = 1.
Figure : as c goes from 1 to 1
6
On the Evolution of Random Graphs
Tipan GTOA March 19, 2014 11 / 18

35. Strategy and Structure Graphs and Behavior
Local Interactions in the Quantitative Social Sciences
Sociologist, Mark Granovetter: The Strength of Weak Ties (1973)
Economists: predictive power of social interactions
Lawrence Blumef (1993), propose using model from statistical
mechanics to understand strategic interactions
Edward Gleaser EtAl 1996, Crime and Social Interactions
Steven Durlauf (1999) asks in PNAS, How can statistical mechanics
contribute to social science?
H. Peyton Young 2001, Individual Strategy and Social Structure: An
Evolutionary Theory of Institutions
7
responsdent driven sampling
8
Social Networks and Gang Violence
Tipan GTOA March 19, 2014 12 / 18

36. Strategy and Structure Graphs and Behavior
Local Interactions in the Quantitative Social Sciences
Sociologist, Mark Granovetter: The Strength of Weak Ties (1973)
Economists: predictive power of social interactions
Lawrence Blumef (1993), propose using model from statistical
mechanics to understand strategic interactions
Edward Gleaser EtAl 1996, Crime and Social Interactions
Steven Durlauf (1999) asks in PNAS, How can statistical mechanics
contribute to social science?
H. Peyton Young 2001, Individual Strategy and Social Structure: An
Evolutionary Theory of Institutions
by 1996, Social Network Analysis: Methods and Applications by Faust
and Wasserman.
More recently sociolgists at Cornell University have been using graph
based sampling methods 7 to do estimations for hidden populations
sociologists like A.V. Papachristos have been using social networks to
understand the crime in Chicago8.
7
responsdent driven sampling
8
Social Networks and Gang Violence
Tipan GTOA March 19, 2014 12 / 18

37. Scale and Complexity The Web is a Network! ...Bipartite Graphs Everywhere!
CrowdSourcing: Power to the People!
Yochai Benkler on Directories and GooglePageRank
channels/categories/directories,
advertisers/campaigns/creatives
Tipan GTOA March 19, 2014 13 / 18

38. Scale and Complexity The Web is a Network! ...Bipartite Graphs Everywhere!
Site Networks and Audiences
Tipan GTOA March 19, 2014 14 / 18

39. Scale and Complexity The Web is a Network! ...Bipartite Graphs Everywhere!
Site Networks and Audiences
Tipan GTOA March 19, 2014 14 / 18

40. Scale and Complexity The Web is a Network! ...Bipartite Graphs Everywhere!
Community Detection
Why understand community structures of complex networks?
Size, problem reduction
Topology, diverse degree distribution
Tipan GTOA March 19, 2014 15 / 18

41. Scale and Complexity The Web is a Network! ...Bipartite Graphs Everywhere!
Community Detection
Why understand community structures of complex networks?
Size, problem reduction
Topology, diverse degree distribution
Biological Sciences Perspective:
network enables the discovery of organization interactions of a
bio-chemical system
Complex Networks as backbone of Complex Systems
Communities enable decomposition into subsystems, modules
Tipan GTOA March 19, 2014 15 / 18

42. Scale and Complexity The Web is a Network! ...Bipartite Graphs Everywhere!
Community Detection
Why understand community structures of complex networks?
Size, problem reduction
Topology, diverse degree distribution
Biological Sciences Perspective:
network enables the discovery of organization interactions of a
bio-chemical system
Complex Networks as backbone of Complex Systems
Communities enable decomposition into subsystems, modules
In online advertising: Feature Extraction!
Tipan GTOA March 19, 2014 15 / 18

43. Scale and Complexity The Web is a Network! ...Bipartite Graphs Everywhere!
The Pinned Random Walk
Definition (PRW)
Let q = (V ;E) be a connected undirected graph. Let P be the transition
probability matrix induced by the incidence matrix, Pij =
Eij
j Eij
. Let 0
be a probability measure on V and P (0;1). We call an pinned random
walk the discrete time stochastic process, Xk, on G that changes measures
k on V according to:
X0 = x0; almost surely
k = k−1P + (1 − )0 (1)
Tipan GTOA March 19, 2014 16 / 18

44. Conclusion
So . . . What is so great about Networks?
Coming out of the woodworks of the systems you deal with within
online advertising, because your systems are Complex!
They are the underlying structures of you advertising systems
They are predictive!
Statisticians are actively working on tools to extract information from
those rich strutures.
Tipan GTOA March 19, 2014 17 / 18

45. Conclusion
Thank You!
Millennial Media
Rosalee MacKinnon
Tipan GTOA March 19, 2014 18 / 18

46. Conclusion
Thank You!
Millennial Media
Rosalee MacKinnon
Rick Daggett
Tipan GTOA March 19, 2014 18 / 18

47. Conclusion
Thank You!
Millennial Media
Rosalee MacKinnon
Rick Daggett
Dr. Jean M. Grow
Tipan GTOA March 19, 2014 18 / 18