Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interplay between Topology and Social Learning over Weak Graphs   We consider a social learning problem, where a network of agents is
interested in selecting one among a finite number of hypotheses. We focus on
weakly-connected graphs where the network is partitioned into a sending part
and a receiving part. The data collected by the agents might be heterogeneous.
For example, some sub-networks might intentionally generate data from a fake
hypothesis in order to influence other agents. The social learning task is
accomplished via a diffusion strategy where each agent: i) updates individually
its belief using its private data; ii) computes a new belief by exponentiating
a linear combination of the log-beliefs of its neighbors. First, we examine
what agents learn over weak graphs (social learning problem). We obtain
analytical formulas for the beliefs at the different agents, which reveal how
the agents' detection capability and the network topology interact to influence
the beliefs. In particular, the formulas allow us to predict when a
leader-follower behavior is possible, where some sending agents can control the
mind of the receiving agents by forcing them to choose a particular hypothesis.
Second, we consider the dual or reverse learning problem that reveals how
agents learned: given a stream of beliefs collected at a receiving agent, we
would like to discover the global influence that any sending component exerts
on this receiving agent (topology learning problem). A remarkable and perhaps
unexpected interplay between social and topology learning is observed: given
$H$ hypotheses and $S$ sending components, topology learning can be feasible
when $H\geq S$. The latter being only a necessary condition, we examine the
feasibility of topology learning for two useful classes of problems. The
analysis reveals that a critical element to enable faithful topology learning
is the diversity in the statistical models of the sending sub-networks.

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The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph