A number of models have been developed for information spread through networks, often for solving the Influence Maximization (IM) problem. IM is the task of choosing a fixed number of nodes to "seed" with information in order to maximize the spread of this information through the network, with applications in areas such as marketing and public health. Most methods for this problem rely heavily on the assumption of known strength of connections between network members (edge weights), which is often unrealistic. In this paper, we develop a likelihood-based approach to estimate edge weights from the fully and partially observed information diffusion paths. We also introduce a broad class of information diffusion models, the general linear threshold (GLT) model, which generalizes the well-known linear threshold (LT) model by allowing arbitrary distributions of node activation thresholds. We then show our weight estimator is consistent under the GLT and some mild assumptions. For the special case of the standard LT model, we also present a much faster expectation-maximization approach for weight estimation. Finally, we prove that for the GLT models, the IM problem can be solved by a natural greedy algorithm with standard optimality guarantees if all node threshold distributions have concave cumulative distribution functions. Extensive experiments on synthetic and real-world networks demonstrate that the flexibility in the choice of threshold distribution combined with the estimation of edge weights significantly improves the quality of IM solutions, spread prediction, and the estimates of the node activation probabilities.

翻译：针对信息在网络中的传播，已有多种模型被提出，通常用于解决影响力最大化问题。影响力最大化旨在选择固定数量的节点作为信息传播的“种子”，以最大化该信息在网络中的传播范围，在市场营销和公共卫生等领域具有重要应用。现有方法大多严重依赖于网络成员间连接强度已知的假设，但这往往不符合实际情况。本文提出了一种基于似然的方法，用于从完全或部分观测到的信息传播路径中估计边权重。同时，我们引入了一类广泛的信息传播模型——广义线性阈值模型，该模型通过允许节点激活阈值服从任意分布，推广了经典的线性阈值模型。我们证明了在广义线性阈值模型及一些温和假设下，所提出的权重估计量具有一致性。针对标准线性阈值模型这一特例，我们还提出了一种更快速的期望最大化方法进行权重估计。最后，我们证明对于广义线性阈值模型，若所有节点的阈值分布均具有凹的累积分布函数，则影响力最大化问题可通过一种自然的贪心算法求解，并具有标准的最优性保证。在合成网络和真实网络上的大量实验表明，阈值分布选择的灵活性结合边权重的估计，显著提升了影响力最大化解决方案的质量、传播预测的准确性以及节点激活概率的估计效果。