Interactions between actors are frequently represented using a network. The latent position model is widely used for analysing network data, whereby each actor is positioned in a latent space. Inferring the dimension of this space is challenging. Often, for simplicity, two dimensions are used or model selection criteria are employed to select the dimension, but this requires choosing a criterion and the computational expense of fitting multiple models. Here the latent shrinkage position model (LSPM) is proposed which intrinsically infers the effective dimension of the latent space. The LSPM employs a Bayesian nonparametric multiplicative truncated gamma process prior that ensures shrinkage of the variance of the latent positions across higher dimensions. Dimensions with non-negligible variance are deemed most useful to describe the observed network, inducing automatic inference on the latent space dimension. While the LSPM is applicable to many network types, logistic and Poisson LSPMs are developed here for binary and count networks respectively. Inference proceeds via a Markov chain Monte Carlo algorithm, where novel surrogate proposal distributions reduce the computational burden. The LSPM's properties are assessed through simulation studies, and its utility is illustrated through application to real network datasets. Open source software assists wider implementation of the LSPM.

翻译：演员之间的互动经常通过网络来表示。潜在位置模型广泛用于分析网络数据，其中每个演员被定位在潜在空间中。推断该空间的维度具有挑战性。通常，为简单起见，使用两个维度或采用模型选择标准来选择维度，但这需要选择标准并承担拟合多个模型的计算开销。本文提出了潜在收缩位置模型（LSPM），该模型固有地推断潜在空间的有效维度。LSPM采用贝叶斯非参数乘法截断伽马过程先验，确保在高维空间中潜在位置的方差收缩。具有不可忽略方差的维度被认为对描述观察到的网络最有用，从而实现对潜在空间维度的自动推断。虽然LSPM适用于许多网络类型，但本文针对二值网络和计数网络分别开发了逻辑和泊松LSPM。推断通过马尔可夫链蒙特卡洛算法进行，其中新颖的替代建议分布减少了计算负担。通过模拟研究评估了LSPM的特性，并通过应用于真实网络数据集说明了其效用。开源软件有助于LSPM的更广泛实施。