Influence maximization and inference of opinion dynamics on complex networks

Abstract

Influence maximization has commonly been studied in the context of strategically allocating resources to agents in a network to maximize the spread of an opinion. In the first part of this thesis, we relate influence maximization to network control and consider a version of an inter-temporal influence maximization problem. Specifically, we study the competition between two external controllers with fixed campaign budgets. In this competition, one or both of the controllers have the flexibility to determine when to start control in order to maximize the share of a desired opinion in a group of agents who exchange opinions on a social network subject to voting dynamics.
We first investigate the inter-temporal influence maximization in a constant-opponent setting where an active controller maximizes its vote share against a known-strategy opponent. Starting with a simplified model where influence starts to be allocated to all agents at the same time, we find that, for short time horizons, maximum influence is achieved by starting relatively later on more heterogeneous networks than in more homogeneous networks, while the opposite holds for long time horizons. Furthermore, by comparing the vote shares achievable via the node-specific optimization where each agent has different starting times and budget allocations with the same-starting-time scenario, we show that strategic allocations of the node-specific optimization are more effective when fewer resources are available to the controller. Apart from the constant-opponent setting, we also explore the game-theoretical setting where both controllers compete to maximize their influence. We find that the controller with budget superiority will start earlier, while the other controller will concentrate its resources in a later stage in order to use limited resources more effectively and achieve some pull-back from its opponent's initial advantage.

In the above, we have assumed either complete or no information about the opponent's strategy in solving the influence maximization problem. However, while the strategy will not always be known in real-world settings, we can infer information by observing the dynamics of opinion exchanges. Furthermore, instead of only passively observing the dynamics for inference, we are interested in influencing the opinion dynamics in such a way that observations can be improved. For this purpose, we propose a framework of strategically influencing a dynamical process with the aim of making hidden parameters more easily inferable. More specifically, we consider a model of networked agents who exchange opinions subject to voting dynamics. Agent dynamics are subject to peer influence and to the influence of two controllers. One of these controllers is treated as passive and we presume its influence is unknown. We then consider a scenario in which the other active controller attempts to infer the passive controller's influence from observations. We explore how the active controller can strategically deploy its own influence to manipulate the dynamics with the aim of accelerating the convergence of its estimates of the opponent. Along with benchmark cases, we then propose two heuristic algorithms for designing optimal influence allocations. We first demonstrate that it is possible to accelerate the inference process by strategically interacting with the network dynamics. Investigating configurations in which optimal control is deployed, we find that agents with higher degrees and larger opponent allocations are harder to predict. Furthermore, even when applying the heuristic algorithms, opponent's influence is typically the harder to predict the more degree-heterogeneous the social network.

In the third part of the thesis, we extend the previous framework from the voter model to the Ising model. Different from the linearity of the voter model, which results in high levels of mathematical tractability, the non-linearity of the Ising model requires different techniques for analysis. By comparing to benchmark cases of equally targeting, we first demonstrate that it is also possible to accelerate the inference by strategically interacting with the non-linear Ising dynamics. We then apply series expansions to obtain an approximation of the optimized influence configurations in the high-temperature region. By using mean-field estimates, we demonstrate the applicability of the method in a more general scenario where real-time tracking of the system is infeasible. Last, by analyzing the optimized influence profiles, we describe heuristics for manipulating the Ising dynamics for faster inference. For example, we show that agents targeted more strongly by the passive field should also be strongly targeted by the active one, so as to even out the inaccuracy for inferring larger values.

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Identifiers

ORCID for Enrico Gerding: orcid.org/0000-0001-7200-552X

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