The latent position model (LPM) is a popular method used in network data analysis where nodes are assumed to be positioned in a $p$-dimensional latent space. The latent shrinkage position model (LSPM) is an extension of the LPM which automatically determines the number of effective dimensions of the latent space via a Bayesian nonparametric shrinkage prior. However, the LSPM reliance on Markov chain Monte Carlo for inference, while rigorous, is computationally expensive, making it challenging to scale to networks with large numbers of nodes. We introduce a variational inference approach for the LSPM, aiming to reduce computational demands while retaining the model's ability to intrinsically determine the number of effective latent dimensions. The performance of the variational LSPM is illustrated through simulation studies and its application to real-world network data. To promote wider adoption and ease of implementation, we also provide open-source code.

翻译：潜在位置模型（LPM）是网络数据分析中常用的一种方法，其假设节点位于一个$p$维潜在空间中。潜在收缩位置模型（LSPM）是LPM的扩展版本，通过贝叶斯非参数收缩先验自动确定潜在空间的有效维度数量。然而，LSPM依赖马尔可夫链蒙特卡洛方法进行推断，虽然具有严密性，但计算成本高，难以扩展至包含大量节点的网络。我们提出了一种针对LSPM的变分推断方法，旨在降低计算需求的同时保留模型内在确定有效潜在维度数量的能力。通过仿真研究及对真实世界网络数据的应用，我们展示了变分LSPM的性能。为促进更广泛的采用与便于实现，我们还提供了开源代码。