Robust Influence Maximization (1601.06551v2)

Abstract: In this paper, we address the important issue of uncertainty in the edge influence probability estimates for the well studied influence maximization problem --- the task of finding $k$ seed nodes in a social network to maximize the influence spread. We propose the problem of robust influence maximization, which maximizes the worst-case ratio between the influence spread of the chosen seed set and the optimal seed set, given the uncertainty of the parameter input. We design an algorithm that solves this problem with a solution-dependent bound. We further study uniform sampling and adaptive sampling methods to effectively reduce the uncertainty on parameters and improve the robustness of the influence maximization task. Our empirical results show that parameter uncertainty may greatly affect influence maximization performance and prior studies that learned influence probabilities could lead to poor performance in robust influence maximization due to relatively large uncertainty in parameter estimates, and information cascade based adaptive sampling method may be an effective way to improve the robustness of influence maximization.

• The paper introduces Robust Influence Maximization (RIM) to address uncertainty in social network influence, proposing to maximize the worst-case ratio of influence spread.
• Two main approaches are developed: a Lower-Upper Greedy Algorithm and novel sampling methods, including adaptive Information Cascade Sampling, to improve robustness by refining probability estimates.
• Empirical results show that parameter uncertainty significantly impacts influence maximization and that adaptive sampling techniques substantially improve robustness compared to prior methods.

Robust Influence Maximization

The paper "Robust Influence Maximization" presents a comprehensive paper in the domain of social network analysis, particularly focusing on the influence maximization problem under uncertainty. This topic is crucial for applications such as viral marketing, outbreak detection, and rumor monitoring, wherein influence maximization is intended to identify key seed nodes in a network that can maximize the spread of information.

Core Concepts and Contributions

The authors introduce the concept of "Robust Influence Maximization" (RIM), a refined approach to tackle the uncertainty inherent to edge influence probability estimation in networks. They propose maximizing the worst-case ratio between the influence spread of a chosen seed set and the optimal seed set amid unknown parameter inputs. This metric, termed as the "robust ratio," seeks to minimize the multiplicative performance gap under the worst-case scenario.

Two primary algorithms are developed in the paper:

1. Lower-Upper Greedy Algorithm: This algorithm computes a solution-dependent bound by analyzing both the lower and upper parameter vectors associated with the intervals of edge influence probabilities.
2. Sampling Methods for Improving RIM: Beyond just a computational approach, the paper explores sampling techniques aimed at refining these probability estimates. They explore uniform sampling and a novel adaptive sampling mechanism, named Information Cascade Sampling. These methods aim to provide a clearer and tighter parameter space that bolsters the robustness of influence maximization tasks.

Analytical Insights

The paper provides a rigorous theoretical analysis suggesting that earlier models with stochastic edge probabilities often succumb to poor performance when faced with high uncertainty. The examination includes:

• Detailed bounds and algorithmic evaluations ensuring the robust ratio has a viable solution-dependent guarantee.
• Challenges highlighted where the best robust ratio could be notably low, driving the necessity for effective sampling strategies.
• Empirical evaluations on datasets like Flixster and NetHEPT, showcasing the practical impact of their proposed methods and confirming their theoretical assertions.

Results and Implications

Empirical results strongly suggest that parameter uncertainty plays a pivotal role in dictating the efficacy of influence maximization efforts. The failure of prior methods due to their inability to handle large-scale uncertainty is well addressed by the proposed adaptive sampling techniques, which exhibit substantial progress in improving robustness.

The paper's implications are significant for both theoretical research and practical applications in AI and network analysis. It charts a path for future developments, primarily in creating more efficient sampling techniques and exploring the intersections of robust optimization within network science.

Conclusion and Future Work

The paper opens the door to numerous potential research avenues. It lays the groundwork for understanding influence maximization under uncertainty and highlights the importance of adaptive techniques in enhancing data-driven models. Future research could explore improving sampling methodologies and exploring robust optimization strategies further. The paper constitutes a critical stepping stone in addressing the big data challenges and refining the quality of robust social influence analysis.