Information Aggregation and Consensus in Networks
Information Aggregation and Consensus in Networks
John N. Tsitsiklis MIT
The Applied Probability Society Markov Lecture October 2009
Overview • Information propagation/aggregation in networks – Engineered versus social networks – Bayesian versus simplistic updates • Review a few key models and results • Is this applied probability? Theoretical AP random graphs
Applied AP ad. campaigns, etc.
Narrative AP “explain” social phenomena
Recreational AP play with toy models
1
Overview Overview Overview Information propagation/aggregationininnetworks networks •• •Information Information propagation/aggregation propagation/aggregation in networks – Engineeredversus versus socialnetworks networks – – Engineered Engineered versus social social networks – Bayesianversus versus simplisticupdates updates – – Bayesian Bayesian versus simplistic simplistic updates Review afew few keymodels models andresults results •• •Review Review a a few key key models and and results Is thisapplied applied probability? •• •Is Is this this applied probability? probability? Theoretical AP Theoretical Theoretical AP AP random graphs random random graphs graphs
Applied AP Applied Applied AP AP ad. campaigns,etc. etc. ad. ad. campaigns, campaigns, etc.
Narrative AP Narrative Narrative AP AP “explain” socialphenomena phenomena “explain” “explain” social social phenomena
Recreational AP Recreational Recreational AP AP play withtoy toy models play play with with toy models models
1 1 1
Overview Overview Overview Overview Information propagation/aggregation in networks •• • •Information Informationpropagation/aggregation propagation/aggregationin networks Information propagation/aggregation ininnetworks networks – Engineered versus social networks – Engineeredversus versussocial socialnetworks networks – –Engineered Engineered versus social networks – Bayesian versus simplistic updates – Bayesianversus versussimplistic simplisticupdates updates – –Bayesian Bayesian versus simplistic updates Review a few key models and results •• • •Review Reviewa fewkey keymodels modelsand andresults results Review a afew few key models and results Is this applied probability? •• • •Is thisapplied appliedprobability? probability? Is Isthis this applied probability? Theoretical AP Theoretical TheoreticalAP AP Theoretical AP random graphs random randomgraphs graphs random graphs
Applied AP Applied AppliedAP AP Applied AP ad. campaigns, etc. ad. ad.campaigns, campaigns,etc. etc. ad. campaigns, etc.
Narrative AP Narrative NarrativeAP AP Narrative AP “explain” social phenomena “explain” “explain”social socialphenomena phenomena “explain” social phenomena
Recreational AP Recreational RecreationalAP AP Recreational AP play with toy models play playwith withtoy toymodels models play with toy models
1 1 1 1
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Why the Power of the Crowd Is Driving the Future of day low price.
07
12
Myopia and Herding • Modeling of jurors
• Language evolution of Crowds? Wisdom or Madness
The Wisdom of Crowds • Charles Mackay (London, 1841): Extraordinary Popular Delusions and the Madness of Crowds
Wisdom versus Herding – “Men, it has been well said, think in herds; it will be seen that they go mad in herds,. . .”
of Rational but Selfish Agents Consensus and Averaging
12
Myopia and Herding • Modeling of jurors
• Language evolution of Crowds? Wisdom or Madness
The Wisdom of Crowds • Charles Mackay (London, 1841): Extraordinary Popular Delusions and the Madness of Crowds
Wisdom versus Herding – “Men, it has been well said, think in herds; it will be seen that they go mad in herds,. . .”
of Rational but Selfish Agents Consensus and Averaging
12
Sensor and other Engineered Networks • Fusion of available information – we get to design the nodes’ behavior
The Basic Setup • Each node i endowed with private information Xi – Nodes form opinions, make decisions – Nodes observe opinions/decisions or receive messages – Nodes update opinions/decisions – Everyone wants a “good”decision; common objective • Questions – Convergence? To what? How fast? Quality of limit? – Does the underlying graph matter? (Tree, acyclic, random,. . .) • Variations
– Hypothesis testing (binary decisions): P(H0 | Xi) – Parameter estimation: E[Y | Xi]
– Optimization: minu E[c(u, Y ) | Xi]
13
The Basic Setup • Each node i endowed with private information Xi – Nodes form opinions, make decisions – Nodes observe opinions/decisions or receive messages – Nodes update opinions/decisions – Everyone wants a “good”decision; common objective • Questions • Social science: postulate update mechanism – Convergence? To what? How fast? Quality of limit? • –Engineering: design/optimize update mechanism Does the underlying graph matter? (Tree, acyclic, random,. . .) • Variations
– Hypothesis testing (binary decisions): P(H0 | Xi) – Parameter estimation: E[Y | Xi]
– Optimization: minu E[c(u, Y ) | Xi]
13
The Basic Setup • Each node i endowed with private information Xi – Nodes form opinions, make decisions – Nodes observe opinions/decisions or receive messages
The Basic Setup
– Nodes update opinions/decisions
• –Each node iwants endowed with private information Xi Everyone a “good”decision; common objective – Nodes form opinions, make decisions • Questions • Social science: postulate update mechanism – Nodes observe opinions/decisions or receive messages – Convergence? To what? How fast? Quality of limit? – Nodes update opinions/decisions • –Engineering: design/optimize update mechanism Does the underlying graph matter? (Tree, acyclic, random,. . .) – Everyone wants a “good”decision; common objective • Variations • Questions – Hypothesis testing (binary decisions): P(H0 | Xi) – Convergence? To what? How fast? Quality of limit? – Parameter estimation: E[Y | Xi] – Does the underlying graph matter? (Tree, acyclic, random,. . .) – Optimization: minu E[c(u, Y ) | Xi] • Variations
13
John N. Tsitsiklis MIT
The Applied Probability Society Markov Lecture October 2009
Overview • Information propagation/aggregation in networks – Engineered versus social networks – Bayesian versus simplistic updates • Review a few key models and results • Is this applied probability? Theoretical AP random graphs
Applied AP ad. campaigns, etc.
Narrative AP “explain” social phenomena
Recreational AP play with toy models
1
Overview Overview Overview Information propagation/aggregationininnetworks networks •• •Information Information propagation/aggregation propagation/aggregation in networks – Engineeredversus versus socialnetworks networks – – Engineered Engineered versus social social networks – Bayesianversus versus simplisticupdates updates – – Bayesian Bayesian versus simplistic simplistic updates Review afew few keymodels models andresults results •• •Review Review a a few key key models and and results Is thisapplied applied probability? •• •Is Is this this applied probability? probability? Theoretical AP Theoretical Theoretical AP AP random graphs random random graphs graphs
Applied AP Applied Applied AP AP ad. campaigns,etc. etc. ad. ad. campaigns, campaigns, etc.
Narrative AP Narrative Narrative AP AP “explain” socialphenomena phenomena “explain” “explain” social social phenomena
Recreational AP Recreational Recreational AP AP play withtoy toy models play play with with toy models models
1 1 1
Overview Overview Overview Overview Information propagation/aggregation in networks •• • •Information Informationpropagation/aggregation propagation/aggregationin networks Information propagation/aggregation ininnetworks networks – Engineered versus social networks – Engineeredversus versussocial socialnetworks networks – –Engineered Engineered versus social networks – Bayesian versus simplistic updates – Bayesianversus versussimplistic simplisticupdates updates – –Bayesian Bayesian versus simplistic updates Review a few key models and results •• • •Review Reviewa fewkey keymodels modelsand andresults results Review a afew few key models and results Is this applied probability? •• • •Is thisapplied appliedprobability? probability? Is Isthis this applied probability? Theoretical AP Theoretical TheoreticalAP AP Theoretical AP random graphs random randomgraphs graphs random graphs
Applied AP Applied AppliedAP AP Applied AP ad. campaigns, etc. ad. ad.campaigns, campaigns,etc. etc. ad. campaigns, etc.
Narrative AP Narrative NarrativeAP AP Narrative AP “explain” social phenomena “explain” “explain”social socialphenomena phenomena “explain” social phenomena
Recreational AP Recreational RecreationalAP AP Recreational AP play with toy models play playwith withtoy toymodels models play with toy models
1 1 1 1
The Wisdom or Madness of Crowds
Deals
Gifts & Wish Lists
Your Account Feedback | Help | Help | Expanded View
Gift Cards
Cart
New ases
Bestsellers
The New York Times® Best Sellers
Libros En Español
|
Close
Your Lists Bargain Books
Textbooks
The Wisdom of Crowds
re available for Amazon Kindle – Amazon’s new wireless reading device. Learn more
rowds (Paperback)
or) "If, years hence, people remember anything about
s to Be a Millionaire?, they will probably remember one..." (more) , bowling stocks, foam strike, United States, ..) er reviews)
Quantity:
1
or Sign in to turn on 1-Click ordering.
Wisdom versus Herding or
igible for FREE Super Saver Shipping er $25. Details
Amazon Prime Free Trial required. Sign up when you check out. Learn More
of Rational but Selfish Agents
mazon.com. Gift-wrap available.
More Buying Choices
ay, June 2? Order it in the next 50 hours and 30 Day Shipping at checkout. Details
used from $5.92
1 collectible from $21.00
111 used & new from $5.59 Have one to sell?
List Price:
)
Our Price: $9.99
Other Offers:
Consensus and Averaging
$24.95
$16.47
5 used & new from $15.02
$24.95
$16.47
91 used & new from $3.39 29 used & new from $5.83
$25.95
$13.63
Share with Friends
formats
free trial of Amazon Prime. Add this eligible textbook to your cart to qualify. Sign up at
Why the Power of the Crowd Is Driving the Future of day low price.
07
12
Myopia and Herding • Modeling of jurors
• Language evolution of Crowds? Wisdom or Madness
The Wisdom of Crowds • Charles Mackay (London, 1841): Extraordinary Popular Delusions and the Madness of Crowds
Wisdom versus Herding – “Men, it has been well said, think in herds; it will be seen that they go mad in herds,. . .”
of Rational but Selfish Agents Consensus and Averaging
12
Myopia and Herding • Modeling of jurors
• Language evolution of Crowds? Wisdom or Madness
The Wisdom of Crowds • Charles Mackay (London, 1841): Extraordinary Popular Delusions and the Madness of Crowds
Wisdom versus Herding – “Men, it has been well said, think in herds; it will be seen that they go mad in herds,. . .”
of Rational but Selfish Agents Consensus and Averaging
12
Sensor and other Engineered Networks • Fusion of available information – we get to design the nodes’ behavior
The Basic Setup • Each node i endowed with private information Xi – Nodes form opinions, make decisions – Nodes observe opinions/decisions or receive messages – Nodes update opinions/decisions – Everyone wants a “good”decision; common objective • Questions – Convergence? To what? How fast? Quality of limit? – Does the underlying graph matter? (Tree, acyclic, random,. . .) • Variations
– Hypothesis testing (binary decisions): P(H0 | Xi) – Parameter estimation: E[Y | Xi]
– Optimization: minu E[c(u, Y ) | Xi]
13
The Basic Setup • Each node i endowed with private information Xi – Nodes form opinions, make decisions – Nodes observe opinions/decisions or receive messages – Nodes update opinions/decisions – Everyone wants a “good”decision; common objective • Questions • Social science: postulate update mechanism – Convergence? To what? How fast? Quality of limit? • –Engineering: design/optimize update mechanism Does the underlying graph matter? (Tree, acyclic, random,. . .) • Variations
– Hypothesis testing (binary decisions): P(H0 | Xi) – Parameter estimation: E[Y | Xi]
– Optimization: minu E[c(u, Y ) | Xi]
13
The Basic Setup • Each node i endowed with private information Xi – Nodes form opinions, make decisions – Nodes observe opinions/decisions or receive messages
The Basic Setup
– Nodes update opinions/decisions
• –Each node iwants endowed with private information Xi Everyone a “good”decision; common objective – Nodes form opinions, make decisions • Questions • Social science: postulate update mechanism – Nodes observe opinions/decisions or receive messages – Convergence? To what? How fast? Quality of limit? – Nodes update opinions/decisions • –Engineering: design/optimize update mechanism Does the underlying graph matter? (Tree, acyclic, random,. . .) – Everyone wants a “good”decision; common objective • Variations • Questions – Hypothesis testing (binary decisions): P(H0 | Xi) – Convergence? To what? How fast? Quality of limit? – Parameter estimation: E[Y | Xi] – Does the underlying graph matter? (Tree, acyclic, random,. . .) – Optimization: minu E[c(u, Y ) | Xi] • Variations
13
