Download - Social Search in Small-World Experiments
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Social Search in Small-
World ExperimentsSharad Goel, Roby Muhamad and Duncan Watts
2009
Akhil Jain
2011CS50274
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Outline
Algorithmic Small World Hypothesis
Work done until now
A new model of attrition
Heterogeneity
Unbiasedness
Results
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Algorithmic Small World Hypothesis
Topological For a randomly chosen pair of individuals,
there exists with high probability a short chain of
intermediaries that connects them.
Algorithmic Ordinary individuals can effectively
navigate these short chains themselves with every
individual having only local knowledge of the social
network in question.
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Topological Studies
A majority of individuals in a given population are
connected in a single giant component.
The typical shortest path length connecting pairs of
nodes within the giant component is of the order of the
logarithm of the system size.
By Daniel' (User:Dannie-walker) (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-
2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
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The problems with algorithmic studies
Reliance on simulations hence not generalizable.
Homogeneity assumption!
Attrition Low rates of chain completion with length
Lack of motivation
Failure to receive the message
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Stochastic modelling of attrition the
story so far
Parameter is the probability of termination at each step.
Two estimators for true length in absence of attrition:
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Problems with such attrition modelling
Existence of multiple small worlds bowl of lumpy
oatmeal!
Search ability is not uniform but a function of social
capital Homogeneity!
Most source-target pairs live in separate populations that
can only be reached via long or undiscoverable paths
Unbiasedness.
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A new model of attritionUnbiased and Heterogeneous estimators
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Experiments
The use of email to allow larger access at reduced cost
1. Dec 2001 Aug 2003; 98865 people from 168 countries
initiated 106295 chains directed at 18 targets in 13
countries 491 (0.5%) reached the target.
2. Aug 2003 Dec 2007; 85621 people from 163 countries
initiated 56033 chains directed at 21 targets in 13
countries 61 (0.1%) reached the target.
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Dealing with heterogeneity
Next step continuance probability
Logistic multi-level regression
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Dealing with heterogeneity
9 categories 66 parameters
Each category is modelled as a normal distribution with 0 mean
Obtain regression coefficients for each attribute value in each category
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A few interesting results
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Dealing with Biasedness
Space of paths that can be observed
P() probability of choosing a path in
Q() probability that path is observed
A missing value is observed with probability ()
Let denote the ith chain observed in the experiment
Without attrition, expected true length is given by = () where f() is the length of path
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Dealing with Biasedness
Let m is the number of paths observed with non missing
values, then an unbiased estimator for the man path
length is given by
This can also be used to find an unbiased estimate for pi the probability that path length is i
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Estimating Chain Lengths
Homogenous Attrition
Uniform for all
Different for the first link in the chain
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Estimating Chain Lengths
Heterogeneous attrition
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Estimating Chain Lengths
Randomised attrition
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Results
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Thank youQuestions?