Cross-View Latent Integration via Nonparametric Gamma Shrinkage Factor Analysis

Factor analysis is a dominant paradigm for multi-omic heterogeneous data, but is challenged by partially redundant signals and noise across views and by an unknown true number of factors. We present CLING, an unsupervised multi-view factor model with hierarchical Bayesian sparsity priors: a product-of-Gammas prior inducing cumulative column-wise shrinkage (increasing with factor index) coupled with a Gamma-Gamma local-precision hierarchy on loadings yielding heavy-tailed marginals. This pairing enables automatic factor selection by adaptively deactivating unsupported factors while retaining active ones during inference, and induces selective sparsity that allows salient loadings to escape shrinkage while collapsing negligible ones. As a fully conjugate hierarchical model, CLING admits a scalable variational inference algorithm for multi-view data. Across synthetic benchmarks and multi-omics datasets, CLING recovers more accurate factors and more informative loadings while explaining at least as much variance as competitive multi-view baselines; on glioblastoma gene expression and DNA methylation data, CLING identifies pathways linked to tumor subtype and patient age.