17,709 research outputs found
Maximizing Welfare in Social Networks under a Utility Driven Influence Diffusion Model
Motivated by applications such as viral marketing, the problem of influence
maximization (IM) has been extensively studied in the literature. The goal is
to select a small number of users to adopt an item such that it results in a
large cascade of adoptions by others. Existing works have three key
limitations. (1) They do not account for economic considerations of a user in
buying/adopting items. (2) Most studies on multiple items focus on competition,
with complementary items receiving limited attention. (3) For the network
owner, maximizing social welfare is important to ensure customer loyalty, which
is not addressed in prior work in the IM literature. In this paper, we address
all three limitations and propose a novel model called UIC that combines
utility-driven item adoption with influence propagation over networks. Focusing
on the mutually complementary setting, we formulate the problem of social
welfare maximization in this novel setting. We show that while the objective
function is neither submodular nor supermodular, surprisingly a simple greedy
allocation algorithm achieves a factor of of the optimum
expected social welfare. We develop \textsf{bundleGRD}, a scalable version of
this approximation algorithm, and demonstrate, with comprehensive experiments
on real and synthetic datasets, that it significantly outperforms all
baselines.Comment: 33 page
Minimizing Seed Set Selection with Probabilistic Coverage Guarantee in a Social Network
A topic propagating in a social network reaches its tipping point if the
number of users discussing it in the network exceeds a critical threshold such
that a wide cascade on the topic is likely to occur. In this paper, we consider
the task of selecting initial seed users of a topic with minimum size so that
with a guaranteed probability the number of users discussing the topic would
reach a given threshold. We formulate the task as an optimization problem
called seed minimization with probabilistic coverage guarantee (SM-PCG). This
problem departs from the previous studies on social influence maximization or
seed minimization because it considers influence coverage with probabilistic
guarantees instead of guarantees on expected influence coverage. We show that
the problem is not submodular, and thus is harder than previously studied
problems based on submodular function optimization. We provide an approximation
algorithm and show that it approximates the optimal solution with both a
multiplicative ratio and an additive error. The multiplicative ratio is tight
while the additive error would be small if influence coverage distributions of
certain seed sets are well concentrated. For one-way bipartite graphs we
analytically prove the concentration condition and obtain an approximation
algorithm with an multiplicative ratio and an
additive error, where is the total number of nodes in the social graph.
Moreover, we empirically verify the concentration condition in real-world
networks and experimentally demonstrate the effectiveness of our proposed
algorithm comparing to commonly adopted benchmark algorithms.Comment: Conference version will appear in KDD 201
Submodular Inference of Diffusion Networks from Multiple Trees
Diffusion and propagation of information, influence and diseases take place
over increasingly larger networks. We observe when a node copies information,
makes a decision or becomes infected but networks are often hidden or
unobserved. Since networks are highly dynamic, changing and growing rapidly, we
only observe a relatively small set of cascades before a network changes
significantly. Scalable network inference based on a small cascade set is then
necessary for understanding the rapidly evolving dynamics that govern
diffusion. In this article, we develop a scalable approximation algorithm with
provable near-optimal performance based on submodular maximization which
achieves a high accuracy in such scenario, solving an open problem first
introduced by Gomez-Rodriguez et al (2010). Experiments on synthetic and real
diffusion data show that our algorithm in practice achieves an optimal
trade-off between accuracy and running time.Comment: To appear in the 29th International Conference on Machine Learning
(ICML), 2012. Website:
http://www.stanford.edu/~manuelgr/network-inference-multitree
Sample Complexity Bounds for Influence Maximization
Influence maximization (IM) is the problem of finding for a given s ? 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 [Kempe et al., 2003]. 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-?)-approximate maximizer with confidence 1-?. Our main result is a surprising upper bound of O(s ? ?^{-2} ln (n/?)) for a broad class of models that includes IC and LT models and their mixtures, where n is the number of nodes and ? is the number of diffusion steps. Generally ? ? n, so this significantly improves over the generic upper bound of O(s n ?^{-2} ln (n/?)). 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-?)-approximate maximizer from simulations and applies to any submodular stochastic diffusion model that satisfies the variance bounds
Defending Elections Against Malicious Spread of Misinformation
The integrity of democratic elections depends on voters' access to accurate
information. However, modern media environments, which are dominated by social
media, provide malicious actors with unprecedented ability to manipulate
elections via misinformation, such as fake news. We study a zero-sum game
between an attacker, who attempts to subvert an election by propagating a fake
new story or other misinformation over a set of advertising channels, and a
defender who attempts to limit the attacker's impact. Computing an equilibrium
in this game is challenging as even the pure strategy sets of players are
exponential. Nevertheless, we give provable polynomial-time approximation
algorithms for computing the defender's minimax optimal strategy across a range
of settings, encompassing different population structures as well as models of
the information available to each player. Experimental results confirm that our
algorithms provide near-optimal defender strategies and showcase variations in
the difficulty of defending elections depending on the resources and knowledge
available to the defender.Comment: Full version of paper accepted to AAAI 201
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