2,467 research outputs found
Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks
We study the outcomes of information aggregation in online social networks. Our main result is that networks with certain realistic structural properties avoid information cascades and enable a population to effectively aggregate information. In our model, each individual in a network holds a private, independent opinion about a product or idea, biased toward a ground truth. Individuals
declare their opinions asynchronously, can observe the stated opinions of their neighbors, and are free to update their declarations over time. Supposing that individuals conform with the majority report of their neighbors, we ask whether the population will eventually arrive at consensus on the ground truth. We show that the answer depends on the network structure: there exist networks for which consensus is unlikely, or for which declarations converge on the incorrect opinion with positive probability. On the other hand, we prove that for networks that are sparse and expansive, the population will converge to the correct opinion with high probability
Distributed Learning from Interactions in Social Networks
We consider a network scenario in which agents can evaluate each other
according to a score graph that models some interactions. The goal is to design
a distributed protocol, run by the agents, that allows them to learn their
unknown state among a finite set of possible values. We propose a Bayesian
framework in which scores and states are associated to probabilistic events
with unknown parameters and hyperparameters, respectively. We show that each
agent can learn its state by means of a local Bayesian classifier and a
(centralized) Maximum-Likelihood (ML) estimator of parameter-hyperparameter
that combines plain ML and Empirical Bayes approaches. By using tools from
graphical models, which allow us to gain insight on conditional dependencies of
scores and states, we provide a relaxed probabilistic model that ultimately
leads to a parameter-hyperparameter estimator amenable to distributed
computation. To highlight the appropriateness of the proposed relaxation, we
demonstrate the distributed estimators on a social interaction set-up for user
profiling.Comment: This submission is a shorter work (for conference publication) of a
more comprehensive paper, already submitted as arXiv:1706.04081 (under review
for journal publication). In this short submission only one social set-up is
considered and only one of the relaxed estimators is proposed. Moreover, the
exhaustive analysis, carried out in the longer manuscript, is completely
missing in this versio
Asynchronous Majority Dynamics in Preferential Attachment Trees
We study information aggregation in networks where agents make binary
decisions (labeled incorrect or correct). Agents initially form independent
private beliefs about the better decision, which is correct with probability
. The dynamics we consider are asynchronous (each round, a single
agent updates their announced decision) and non-Bayesian (agents simply copy
the majority announcements among their neighbors, tie-breaking in favor of
their private signal).
Our main result proves that when the network is a tree formed according to
the preferential attachment model \cite{BarabasiA99}, with high probability,
the process stabilizes in a correct majority within
rounds. We extend our results to other tree structures, including balanced
-ary trees for any .Comment: ICALP 202
Consensus in the Presence of Multiple Opinion Leaders: Effect of Bounded Confidence
The problem of analyzing the performance of networked agents exchanging
evidence in a dynamic network has recently grown in importance. This problem
has relevance in signal and data fusion network applications and in studying
opinion and consensus dynamics in social networks. Due to its capability of
handling a wider variety of uncertainties and ambiguities associated with
evidence, we use the framework of Dempster-Shafer (DS) theory to capture the
opinion of an agent. We then examine the consensus among agents in dynamic
networks in which an agent can utilize either a cautious or receptive updating
strategy. In particular, we examine the case of bounded confidence updating
where an agent exchanges its opinion only with neighboring nodes possessing
'similar' evidence. In a fusion network, this captures the case in which nodes
only update their state based on evidence consistent with the node's own
evidence. In opinion dynamics, this captures the notions of Social Judgment
Theory (SJT) in which agents update their opinions only with other agents
possessing opinions closer to their own. Focusing on the two special DS
theoretic cases where an agent state is modeled as a Dirichlet body of evidence
and a probability mass function (p.m.f.), we utilize results from matrix
theory, graph theory, and networks to prove the existence of consensus agent
states in several time-varying network cases of interest. For example, we show
the existence of a consensus in which a subset of network nodes achieves a
consensus that is adopted by follower network nodes. Of particular interest is
the case of multiple opinion leaders, where we show that the agents do not
reach a consensus in general, but rather converge to 'opinion clusters'.
Simulation results are provided to illustrate the main results.Comment: IEEE Transactions on Signal and Information Processing Over Networks,
to appea
Asynchronous Majority Dynamics on Binomial Random Graphs
We study information aggregation in networks when agents interact to learn a
binary state of the world. Initially each agent privately observes an
independent signal which is "correct" with probability for
some . At each round, a node is selected uniformly at random to
update their public opinion to match the majority of their neighbours (breaking
ties in favour of their initial private signal). Our main result shows that for
sparse and connected binomial random graphs the process
stabilizes in a "correct" consensus in steps
with high probability. In fact, when the process
terminates at time , where is the first time
when all nodes have been selected at least once. However, in dense binomial
random graphs with , there is an information cascade where the
process terminates in the "incorrect" consensus with probability bounded away
from zero
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