A hyperspherical deep Bayesian model for interpretable clustering and relationship prediction in microbiome multi-omics integration

The microbiome plays a significant role in the development and progression of many diseases, yet extracting interpretable insights from multi-omics data remains challenging. Existing approaches face a recurring practical trade-off: deep learning methods achieve high predictive performance but lack uncertainty quantification, whereas probabilistic methods provide interpretable results but require data-type-specific likelihood functions that limit generalization across diverse omics modalities. Here, we introduce DBayesCM (Deep Bayesian Clustering for Multi-omics), which combines deep learning modeling with Bayesian nonparametric methods. DBayesCM employs separate encoders to project microbiome and host omics data into a shared latent space, where an infinite mixture model with a Dirichlet process prior determines the number of clusters automatically while quantifying the uncertainty of each samples assignment. Spike-and-slab priors identify discriminative features, and a Bayesian neural network estimates probabilistic co-occurrence between microbial species and host omics features. To isolate the effect of latent geometry, we evaluate two variants that are identical except for their latent space: DBayesCM-vMF constrains the latent to the unit hypersphere and applies a von Mises-Fisher mixture, while DBayesCM-GMM uses a Euclidean latent space and a Gaussian mixture. On simulated data, the hyperspherical variant recovered the correct number of clusters, whereas the Euclidean variant over-segmented, demonstrating that the latent geometry affects cluster recovery. Applied to colon, breast, and kidney cancer cohorts spanning metagenomics, host metabolomics, RNA-seq, and miRNA data, and to an obstructive sleep apnea model, DBayesCM ranked consistently among the existing methods while uniquely combining data-driven cluster-number determination, sample-level uncertainty, and interpretable feature selection within a single framework. DBayesCM reveals conditional probabilistic co-occurrence between core microbial species and host omics features, enabling uncertainty-aware exploration of microbiome-host relationships across diverse diseases.