Interpretable multi-omics integration across mixed-order tensors with MANTRA.

The integration of multi-modal molecular data is crucial for understanding complex diseases, but existing methods struggle with modern experimental designs that generate datasets with mixed-order tensors-for example, a third-order drug-response tensor alongside a second-order transcriptomics matrix. Here, we present MANTRA (Multi-view ANalysis with Tensor and matRix Alignment), a probabilistic framework that integrates collections of tensors of different orders, combining the strengths of group factor analysis and tensor decomposition. MANTRA learns interpretable latent factors and naturally handles missing data through a Bayesian approach with structured sparsity priors. On a Chronic Lymphocytic Leukemia (CLL) dataset, the joint analysis of a third-order drug-response tensor and a second-order RNA-seq matrix with MANTRA revealed clinically relevant patient subgroups that were missed by single-view or matrix-based analyses. In a single-cell multi-omics study of Acute Lymphoblastic Leukemia (ALL), MANTRA identified a novel patient subgroup defined by a distinct molecular program in plasmacytoid dendritic cells (pDCs), linking disease heterogeneity to a specific cell type. By explicitly modeling higher- order data structures, MANTRA provides an interpretable tool to uncover hidden biological variation from complex experimental data.