An important issue in social network analysis refers to the development of algorithms for estimating parameters of a social network model, using data available from the network itself. This entails solving an optimization problem. In the paper, we propose a new method for parameter estimation in a specific social network model, namely, the so‐called p‐star random graph model with three parameters. The method is based on the mean‐field approximation of the moments associated with the three subgraphs defining the model, namely: the mean numbers of edges, 2‐stars, and triangles. A modified gradient ascent method is applied to maximize the log‐likelihood function of the p‐star model, in which the components of the gradient are computed using approximate values of the moments. Compared to other existing iterative methods for parameter estimation, which are computationally very expensive when the number of vertices becomes large, such as gradient ascent applied to maximum log‐likelihood and maximum log‐pseudo‐likelihood estimation, the proposed approach has the advantage of a much cheaper cost per iteration, which is practically independent of the number of vertices.

中文翻译：

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3参数p星随机图模型中的参数估计

社交网络分析中的一个重要问题是使用可从网络本身获得的数据来开发用于估算社交网络模型参数的算法。这需要解决优化问题。在本文中，我们提出了一种在特定社交网络模型中进行参数估计的新方法，即具有三个参数的所谓的p星随机图模型。该方法基于与定义模型的三个子图相关联的矩的均值场近似，即：边，2星和三角形的均值。一种改进的梯度上升方法被应用来最大化p的对数似然函数-星模型，其中使用矩的近似值计算梯度的分量。与其他现有的用于参数估计的迭代方法相比，当顶点数量变大时，该方法在计算上非常昂贵，例如将梯度上升应用于最大对数似然和最大对数伪似然估计，该方法具有以下优点：每次迭代的成本要便宜得多，实际上与顶点数无关。