Graph-Aligned Random Partition Model (GARP)
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Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the biological relations of the clusters. The increasing availability of large genomic data requires new statistical tools to perform model-based clustering and infer the relationship between homogeneous subgroups of units. Motivated by single-cell RNA applications we develop a novel dependent mixture model to jointly perform cluster analysis and align the clusters on a graph. Our flexible graph-aligned random partition model (GARP) exploits Gibbs-type priors as building blocks, allowing us to derive analytical results on the graph-aligned random partition's probability mass function (pmf). We derive a generalization of the Chinese restaurant process from the pmf and a related efficient and neat MCMC algorithm to perform Bayesian inference. We perform posterior inference on real single-cell RNA data from mice stem cells. We further investigate the performance of our model in capturing the underlying clustering structure as well as the underlying graph by means of simulation studies.
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