Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle modern large-scale networks. To overcome this limitation, we introduce a new prior for continuous-time LSMs based on Bayesian P-splines that allows the posterior to adapt to the dimension of the latent space and the temporal variation in each latent position. We propose a stochastic variational inference algorithm to estimate the model parameters. We use stochastic optimization to subsample both dyads and observed time points to design a fast algorithm that is linear in the number of edges in the dynamic network. Furthermore, we establish non-asymptotic error bounds for point estimates derived from the variational posterior. To our knowledge, this is the first such result for Bayesian estimators of continuous-time LSMs. Lastly, we use the method to analyze a large data set of international conflicts consisting of 4,456,095 relations from 2018 to 2022.

翻译：潜空间模型常用于分析随时间连续演变的动态（时变）网络。现有贝叶斯推断方法依赖马尔可夫链蒙特卡洛算法，无法处理现代大规模网络。为突破这一局限，我们提出一种基于贝叶斯P样条的连续时间潜空间模型新先验，使后验能够自适应调整潜空间维度与各潜位置的时间变化率。我们设计随机变分推断算法进行模型参数估计，通过随机优化对二元组和观测时间点进行子采样，构建与动态网络边数呈线性关系的快速算法。此外，我们建立了变分后验点估计的非渐近误差界。据我们所知，这是连续时间潜空间模型贝叶斯估计器的首个此类结果。最后，我们将该方法用于分析2018至2022年间包含4,456,095条关系的国际冲突大规模数据集。