Post on 30-Aug-2020
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CS 886 Advanced Topics in Artificial Intelligence: Multiagent Systems
Rank Aggregation Methods for the WebCynthia Dwork Ravi Kumar Moni Naor D. Sivakumar
Presented by: Wanying Luo
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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What is rank aggregation problem
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Based on different ranking techniques and criteria, we may get different results
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What is rank aggregation problem
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Need to obtain a ”consensus” ranking of all the individual rankings
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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Motivation
Provide robust meta searchExamples of meta search engines
ClustyDogpileMetacrawler
Spamhttp://searchenginewatch.com/showPage.html?page=3483601
Commercial interests, e.g., sponsored links
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Motivation
Provide robust meta searchExamples of meta search engines
ClustyDogpileMetacrawler
Spamhttp://searchenginewatch.com/showPage.html?page=3483601
Commercial interests, e.g., sponsored links
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Motivation
Provide robust meta searchExamples of meta search engines
ClustyDogpileMetacrawler
Spamhttp://searchenginewatch.com/showPage.html?page=3483601
Commercial interests, e.g., sponsored links
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Motivation
User may provide a variety of searching criteria
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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Challenges
Unrealistic to rank the entire collection of pages on the web
29.7 billion pages on the World Wide Web as of February 2007 (http://www.boutell.com/)
Most search engines rank only the top few hundred entries
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Challenges
Unrealistic to rank the entire collection of pages on the web
29.7 billion pages on the World Wide Web as of February 2007 (http://www.boutell.com/)
Most search engines rank only the top few hundred entries
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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Preliminaries
Ordered listGiven a universe U, an ordered list τ with respect to U is anordering(aka ranking) of a subset S ⊆ U, i.e.
τ=[χ1 ≥ χ2 ≥ …≥ χd ]
Full listτ contains all the elements in U
Partial list|τ| < |U|
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Preliminaries
Ordered listGiven a universe U, an ordered list τ with respect to U is anordering(aka ranking) of a subset S ⊆ U, i.e.
τ=[χ1 ≥ χ2≥ …≥ χd ]
Full listτ contains all the elements in U
Partial list|τ| < |U|
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Preliminaries
Ordered listGiven a universe U, an ordered list τ with respect to U is anordering(aka ranking) of a subset S ⊆ U, i.e.
τ=[χ1 ≥ χ2≥ …≥ χd ]
Full listτ contains all the elements in U
Partial list|τ| < |U|
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Preliminaries
Rank aggregation approachGoal: minimize the total disagreement between several rankings Spearman footrule distance
Given two full lists σ and τ, F(σ,τ)=Σi=1|σ(i)-τ(i)|Kendall tau distance
Given two full lists σ and τ, K(σ,τ)=|{(i,j) | i<j, σ(i)<σ(j) but τ(i)>τ(j) }|These two measurements can be generalized to several listsCan also be generalized to partial lists
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Preliminaries
Rank aggregation approachGoal: minimize the total disagreement between several rankings Spearman footrule distance
Given two full lists σ and τ, F(σ,τ)=Σi=1|σ(i)-τ(i)|Kendall tau distance
Given two full lists σ and τ, K(σ,τ)=|{(i,j) | i<j, σ(i)<σ(j) but τ(i)>τ(j) }|These two measurements can be generalized to several listsCan also be generalized to partial lists
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Preliminaries
Rank aggregation approachGoal: minimize the total disagreement between several rankings Spearman footrule distance
Given two full lists σ and τ, F(σ,τ)=Σi=1|σ(i)-τ(i)|Kendall tau distance
Given two full lists σ and τ, K(σ,τ)=|{(i,j) | i<j, σ(i)<σ(j) but τ(i)>τ(j) }|These two measurements can be generalized to several listsCan also be generalized to partial lists
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Preliminaries
Rank aggregation approachGoal: minimize the total disagreement between several rankings Spearman footrule distance
Given two full lists σ and τ, F(σ,τ)=Σi=1|σ(i)-τ(i)|Kendall tau distance
Given two full lists σ and τ, K(σ,τ)=|{(i,j) | i<j, σ(i)<σ(j) but τ(i)>τ(j) }|These two measurements can be generalized to several listsCan also be generalized to partial lists
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Preliminaries
Rank aggregation approachGoal: minimize the total disagreement between several rankings Spearman footrule distance
Given two full lists σ and τ, F(σ,τ)=Σi=1|σ(i)-τ(i)|Kendall tau distance
Given two full lists σ and τ, K(σ,τ)=|{(i,j) | i<j, σ(i)<σ(j) but τ(i)>τ(j) }|These two measurements can be generalized to several listsCan also be generalized to partial lists
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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First result: spam resistance in meta-search
Extended Condorcet Criterion (ECC) If there is a partition (C, C’) of S such that for any x∈Cand y∈C’ the majority prefers x to y, then x must be ranked above y
ECC can be used to fight spam in meta-searchHow to achieve ECC efficiently
Local Kemenization method
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First result: spam resistance in meta-search
Extended Condorcet Criterion (ECC) If there is a partition (C, C’) of S such that for any x∈Cand y∈C’ the majority prefers x to y, then x must be ranked above y
ECC can be used to fight spam in meta-searchHow to achieve ECC efficiently
Local Kemenization method
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First result: spam resistance in meta-search
Extended Condorcet Criterion (ECC) If there is a partition (C, C’) of S such that for any x∈Cand y∈C’ the majority prefers x to y, then x must be ranked above y
ECC can be used to fight spam in meta-searchHow to achieve ECC efficiently
Local Kemenization method
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First result: spam resistance in meta-search
An example to illustrate Local Kemenization …
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First result: spam resistance in meta-search
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First result: spam resistance in meta-search
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First result: spam resistance in meta-search
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B>A A>B B>A
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First result: spam resistance in meta-search
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First result: spam resistance in meta-search
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First result: spam resistance in meta-search
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A>D A>D A>D
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First result: spam resistance in meta-search
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First result: spam resistance in meta-search
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First result: spam resistance in meta-search
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C is preferred to D in two lists
D is preferred to C in one list
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C>D D>C C>D
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First result: spam resistance in meta-search
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First result: spam resistance in meta-search
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A>C A>C C>A
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First result: spam resistance in meta-search
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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Second result: Markov chain methods
Markov chain A set of states S={1,2,...,n}An n x n matrix MBegins with an initial state xAt each step the system moves from state i to state j with probability Mij
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Second result: Markov chain methods
Under some nice condition, system eventually reaches a fixed point irrespective of the initial state x
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Second result: Markov chain methods
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Original rankings
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Second result: Markov chain methods
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0.1 0.1 0.3 0.3
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Original rankings
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Second result: Markov chain methods
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Original rankings Aggregated ranking
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Second result: Markov chain methods
Assume the current state is page PMC1: The next state is chosen uniformly from the multiset of all pages that were ranked higher than or equal to P by some search engine that ranked PPlease refer to the paper for the rest …
MC2MC3
MC4
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Second result: Markov chain methods
Assume the current state is page PMC1: The next state is chosen uniformly from the multiset of all pages that were ranked higher than or equal to P by some search engine that ranked PPlease refer to the paper for the rest …
MC2MC3MC4
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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Applications
Meta-searchSpam reductionMulti-criteria searchSearch engine comparison
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Applications
Meta-searchSpam reductionMulti-criteria searchSearch engine comparison
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Applications
Meta-searchSpam reductionMulti-criteria searchSearch engine comparison
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Applications
Meta-searchSpam reductionMulti-criteria searchSearch engine comparison
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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Experiments
Experiments were conducted by using the following search engines: Altavista(AV), Alltheweb(AW), Excite(EX), Google(GG), Hotbot(HB), Lycos(LY) and Northernlight(NL)Experiment on meta-search using several keywords: “affirmative action”, alcoholism, sushi, ...
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Experiments
Experiments were conducted by using the following search engines: Altavista(AV), Alltheweb(AW), Excite(EX), Google(GG), Hotbot(HB), Lycos(LY) and Northernlight(NL)Experiment on meta-search using several keywords: “affirmative action”, alcoholism, sushi, ...
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Experiments
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Experiments
SFO and MC4 outperform the other 4 algorithms
MC4 performs better than SFO most of the time
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Experiments
Experiment on spam reduction using queries: Feng shui, organic vegetable, gardening
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Experiments
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Experiments
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Experiments
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Experiments
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Experiments
Local Kemenization works!
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Outline
What is rank aggregation problemMotivationChallengesPreliminariesFirst result: spam resistance in meta-searchSecond result: Markov chain methodsApplicationsExperimentsConclusion
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Conclusion
Proposed several rank aggregation techniques using Markov chainEstablished the value of Extended CondorcetCriterion (ECC)
Spam resistanceFuture work
Obtain a qualitative understanding of why Markov chain methods perform well
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Conclusion
Proposed several rank aggregation techniques using Markov chainEstablished the value of Extended CondorcetCriterion (ECC)
Spam resistanceFuture work
Obtain a qualitative understanding of why Markov chain methods perform well
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Conclusion
Proposed several rank aggregation techniques using Markov chainEstablished the value of Extended CondorcetCriterion (ECC)
Spam resistanceFuture work
Obtain a qualitative understanding of why Markov chain methods perform well
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Questions???