  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.
