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- 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

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