Neural Information Processing Systems http://nips.cc/

We establish upper and lower bounds for the influence of a set of nodes in certain types of contagion models. We derive two sets of bounds, the first designed for linear threshold models, and the second more broadly applicable to a general class of triggering models, which subsumes the popular independent cascade models, as well. We quantify the gap between our upper and lower bounds in the case of the linear threshold model and illustrate the gains of our upper bounds for independent cascade models in relation to existing results. Importantly, our lower bounds are monotonic and submodular, implying that a greedy algorithm for influence maximization is guaranteed to produce a maximizer within a 1 1e -factor of the truth. Although the problem of exact influence computation is NP-hard in general, our bounds may be evaluated efficiently. This leads to an attractive, highly scalable algorithm for influence maximization with rigorous theoretical guarantees.

Neural Information Processing Systems http://nips.cc/

The influence maximization (IM) problem aims to identify a budgeted set of nodes with the highest potential to influence the largest number of users in a cascade model, a key challenge in viral marketing. Traditional \emph{IM} approaches consider each user/node independently as a potential target customer. However, in many scenarios, the target customers comprise motifs, where activating only one or a few users within a motif is insufficient for effective viral marketing, which, nevertheless, receives little attention. For instance, if a motif of three friends planning to dine together, targeting all three simultaneously is crucial for a restaurant advertisement to succeed.In this paper, we address the motif-oriented influence maximization problem under the linear threshold model. We prove that the motif-oriented IM problem is NP-hard and that the influence function is neither supermodular nor submodular, in contrast to the classical \emph{IM} setting.To simplify the problem, we establish the submodular upper and lower bounds for the influence function. By leveraging the submodular property, we propose a natural greedy strategy that simultaneously maximizes both bounds. Our algorithm has an approximation ratio of $\tau\cdot (1-1/e-\varepsilon)$ and a near-linear time complexity of $O((k+l)(m+\eta)\log \eta/\varepsilon^2)$.Experimental results on diverse datasets confirm the effectiveness of our approach in motif maximization.

We consider the canonical problem of influence maximization in social networks. Since the seminal work of Kempe, Kleinberg, and Tardos there have been two, largely disjoint efforts on this problem. The first studies the problem associated with learning the generative model that produces cascades, and the second focuses on the algorithmic challenge of identifying a set of influencers, assuming the generative model is known. Recent results on learning and optimization imply that in general, if the generative model is not known but rather learned from training data, no algorithm for influence maximization can yield a constant factor approximation guarantee using polynomially-many samples, drawn from any distribution. In this paper we describe a simple algorithm for maximizing influence from training data. The main idea behind the algorithm is to leverage the strong community structure of social networks and identify a set of individuals who are influentials but whose communities have little overlap. Although in general, the approximation guarantee of such an algorithm is unbounded, we show that this algorithm performs well experimentally. To analyze its performance, we prove this algorithm obtains a constant factor approximation guarantee on graphs generated through the stochastic block model, traditionally used to model networks with community structure.

We establish upper and lower bounds for the influence of a set of nodes in certain types of contagion models. We derive two sets of bounds, the first designed for linear threshold models, and the second more broadly applicable to a general class of triggering models, which subsumes the popular independent cascade models, as well. We quantify the gap between our upper and lower bounds in the case of the linear threshold model and illustrate the gains of our upper bounds for independent cascade models in relation to existing results. Importantly, our lower bounds are monotonic and submodular, implying that a greedy algorithm for influence maximization is guaranteed to produce a maximizer within a (1 - 1/e)-factor of the truth. Although the problem of exact influence computation is NP-hard in general, our bounds may be evaluated efficiently. This leads to an attractive, highly scalable algorithm for influence maximization with rigorous theoretical guarantees.

Traditional IM approaches consider each user/node independently as a potential target customer.

Neural Information Processing Systems http://nips.cc/