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Register a new userOnline Influence Maximization in Non-Stationary Social Networks
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Yixin Bao
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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Social networks have been popular platforms for information propagation. An important use case is viral marketing: given a promotion budget, an advertiser can choose some influential users as the seed set and provide them free or discounted sample products; in this way, the advertiser hopes to increase the popularity of the product in the users friend circles by the world-of-mouth effect, and thus maximizes the number of users that information of the production can reach. There has been a body of literature studying the influence maximization problem. Nevertheless, the existing studies mostly investigate the problem on a one-off basis, assuming fixed known influence probabilities among users, or the knowledge of the exact social network topology. In practice, the social network topology and the influence probabilities are typically unknown to the advertiser, which can be varying over time, i.e., in cases of newly established, strengthened or weakened social ties. In this paper, we focus on a dynamic non-stationary social network and design a randomized algorithm, RSB, based on multi-armed bandit optimization, to maximize influence propagation over time. The algorithm produces a sequence of online decisions and calibrates its explore-exploit strategy utilizing outcomes of previous decisions. It is rigorously proven to achieve an upper-bounded regret in reward and applicable to large-scale social networks. Practical effectiveness of the algorithm is evaluated using both synthetic and real-world datasets, which demonstrates that our algorithm outperforms previous stationary methods under non-stationary conditions.
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We study the online influence maximization (OIM) problem in social networks, where in multiple rounds the learner repeatedly chooses seed nodes to generate cascades, observes the cascade feedback, and gradually learns the best seeds that generate the largest cascade. We focus on two major challenges in this paper. First, we work with node-level feedback instead of edge-level feedback. The edge-level feedback reveals all edges that pass through information in a cascade, where the node-level feedback only reveals the activated nodes with timestamps. The node-level feedback is arguably more realistic since in practice it is relatively easy to observe who is influenced but very difficult to observe from which relationship (edge) the influence comes from. Second, we use standard offline oracle instead of offline pair-oracle. To compute a good seed set for the next round, an offline pair-oracle finds the best seed set and the best parameters within the confidence region simultaneously, and such an oracle is difficult to compute due to the combinatorial core of OIM problem. So we focus on how to use the standard offline influence maximization oracle which finds the best seed set given the edge parameters as input. In this paper, we resolve these challenges for the two most popular diffusion models, the independent cascade (IC) and the linear threshold (LT) model. For the IC model, the past research only achieves edge-level feedback, while we present the first $widetilde{O}(sqrt{T})$-regret algorithm for the node-level feedback. Besides, the algorithm only invokes standard offline oracles. For the LT model, a recent study only provides an OIM solution that meets the first challenge but still requires a pair-oracle. In this paper, we apply a similar technique as in the IC model to replace the pair-oracle with a standard oracle while maintaining $widetilde{O}(sqrt{T})$-regret.
Activity maximization is a task of seeking a small subset of users in a given social network that makes the expected total activity benefit maximized. This is a generalization of many real applications. In this paper, we extend activity maximization problem to that under the general marketing strategy $vec{x}$, which is a $d$-dimensional vector from a lattice space and has probability $h_u(vec{x})$ to activate a node $u$ as a seed. Based on that, we propose the continuous activity maximization (CAM) problem, where the domain is continuous and the seed set we select conforms to a certain probability distribution. It is a new topic to study the problem about information diffusion under the lattice constraint, thus, we address the problem systematically here. First, we analyze the hardness of CAM and how to compute the objective function of CAM accurately and effectively. We prove this objective function is monotone, but not DR-submodular and not DR-supermodular. Then, we develop a monotone and DR-submodular lower bound and upper bound of CAM, and apply sampling techniques to design three unbiased estimators for CAM, its lower bound and upper bound. Next, adapted from IMM algorithm and sandwich approximation framework, we obtain a data-dependent approximation ratio. This process can be considered as a general method to solve those maximization problem on lattice but not DR-submodular. Last, we conduct experiments on three real-world datasets to evaluate the correctness and effectiveness of our proposed algorithms.
Influence maximization (IM) aims at maximizing the spread of influence by offering discounts to influential users (called seeding). In many applications, due to users privacy concern, overwhelming network scale etc., it is hard to target any user in the network as one wishes. Instead, only a small subset of users is initially accessible. Such access limitation would significantly impair the influence spread, since IM often relies on seeding high degree users, which are particularly rare in such a small subset due to the power-law structure of social networks. In this paper, we attempt to solve the limited IM in real-world scenarios by the adaptive approach with seeding and diffusion uncertainty considered. Specifically, we consider fine-grained discounts and assume users accept the discount probabilistically. The diffusion process is depicted by the independent cascade model. To overcome the access limitation, we prove the set-wise friendship paradox (FP) phenomenon that neighbors have higher degree in expectation, and propose a two-stage seeding model with the FP embedded, where neighbors are seeded. On this basis, for comparison we formulate the non-adaptive case and adaptive case, both proven to be NP-hard. In the non-adaptive case, discounts are allocated to users all at once. We show the monotonicity of influence spread w.r.t. discount allocation and design a two-stage coordinate descent framework to decide the discount allocation. In the adaptive case, users are sequentially seeded based on observations of existing seeding and diffusion results. We prove the adaptive submodularity and submodularity of the influence spread function in two stages. Then, a series of adaptive greedy algorithms are proposed with constant approximation ratio.
Online social networks have been one of the most effective platforms for marketing and advertising. Through word of mouth effects, information or product adoption could spread from some influential individuals to millions of users in social networks. Given a social network $G$ and a constant $k$, the influence maximization problem seeks for $k$ nodes in $G$ that can influence the largest number of nodes. This problem has found important applications, and a large amount of works have been devoted to identifying the few most influential users. But most of existing works only focus on the diffusion of a single idea or product in social networks. However, in reality, one company may produce multiple kinds of products and one user may also have multiple adoptions. Given multiple kinds of different products with different activation costs and profits, it is crucial for the company to distribute the limited budget among multiple products in order to achieve profit maximization. Profit Maximization with Multiple Adoptions (PM$^{2}$A) problem aims to seek for a seed set within the budget to maximize the overall profit. In this paper, a Randomized Modified Greedy (RMG) algorithm based on the Reverse Influence Sampling (RIS) technique is presented for the PM$^{2}$A problem, which could achieve a $(1-1/e-varepsilon)$-approximate solution with high probability. Compared with the algorithm proposed in [16] that achieves a $frac{1}{2}(1-1/e^{2})$-approximate solution, our algorithm provides a better performance ratio which is also the best performance ratio of the PM$^{2}$A problem. Comprehensive experiments on three real-world social networks are conducted, and the results demonstrate that our RMG algorithm outperforms the algorithm proposed in [16] and other heuristics in terms of profit maximization, and could better allocate the budget.
Influence Maximization (IM) aims to maximize the number of people that become aware of a product by finding the `best set of `seed users to initiate the product advertisement. Unlike prior arts on static social networks containing fixed number of users, we undertake the first study of IM in more realistic evolving networks with temporally growing topology. The task of evolving IM ({bfseries EIM}), however, is far more challenging over static cases in the sense that seed selection should consider its impact on future users and the probabilities that users influence one another also evolve over time. We address the challenges through $mathbb{EIM}$, a newly proposed bandit-based framework that alternates between seed nodes selection and knowledge (i.e., nodes growing speed and evolving influences) learning during network evolution. Remarkably, $mathbb{EIM}$ involves three novel components to handle the uncertainties brought by evolution:
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