Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sample Complexity Bounds for Influence Maximization   Influence maximization (IM) is the problem of finding for a given $s\geq 1$ a
set $S$ of $|S|=s$ nodes in a network with maximum influence. With stochastic
diffusion models, the influence of a set $S$ of seed nodes is defined as the
expectation of its reachability over simulations, where each simulation
specifies a deterministic reachability function. Two well-studied special cases
are the Independent Cascade (IC) and the Linear Threshold (LT) models of Kempe,
Kleinberg, and Tardos. The influence function in stochastic diffusion is
unbiasedly estimated by averaging reachability values over i.i.d. simulations.
We study the IM sample complexity: the number of simulations needed to
determine a $(1-\epsilon)$-approximate maximizer with confidence $1-\delta$.
Our main result is a surprising upper bound of $O( s \tau \epsilon^{-2} \ln
\frac{n}{\delta})$ for a broad class of models that includes IC and LT models
and their mixtures, where $n$ is the number of nodes and $\tau$ is the number
of diffusion steps. Generally $\tau \ll n$, so this significantly improves over
the generic upper bound of $O(s n \epsilon^{-2} \ln \frac{n}{\delta})$. Our
sample complexity bounds are derived from novel upper bounds on the variance of
the reachability that allow for small relative error for influential sets and
additive error when influence is small. Moreover, we provide a data-adaptive
method that can detect and utilize fewer simulations on models where it
suffices. Finally, we provide an efficient greedy design that computes an
$(1-1/e-\epsilon)$-approximate maximizer from simulations and applies to any
submodular stochastic diffusion model that satisfies the variance bounds.

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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: hep-th