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Bayesian mixture models are widely used for clustering of high-dimensionaldata with appropriate uncertainty quantification. However, as the dimension ofthe observations increases, posterior inference often tends to favor too manyor too few clusters. This article explains this behavior by studying the randompartition posterior in a non-standard setting with a fixed sample size andincreasing data dimensionality. We provide conditions under which the finitesample posterior tends to either assign every observation to a differentcluster or all observations to the same cluster as the dimension grows.Interestingly, the conditions do not depend on the choice of clustering prior,as long as all possible partitions of observations into clusters have positiveprior probabilities, and hold irrespective of the true data-generating model.We then propose a class of latent mixtures for Bayesian clustering (Lamb) on aset of low-dimensional latent variables inducing a partition on the observeddata. The model is amenable to scalable posterior inference and we show that itcan avoid the pitfalls of high-dimensionality under mild assumptions. Theproposed approach is shown to have good performance in simulation studies andan application to inferring cell types based on scRNAseq.

Escaping the curse of dimensionality in Bayesian model based clustering