The name MANTRA stands for Multi-view ANalysis with Tensor and matRix Alignment, and the framework was developed by Kevin De Azevedo, Yusuf Berk Oruc, and Florian Buettner, who contributed to the German Cancer Consortium and the Frankfurt Cancer Institute. Conceptually, MANTRA can be understood as a generalization of group factor analysis to tensor-valued data, or conversely, as an extension of classical tensor decomposition into the multi-view setting. It takes as input a collection of datasets, some three-dimensional and some two-dimensional, and decomposes them jointly into shared low-dimensional latent factors. Each mode of the data, whether patients, drugs, cytokines, cell types, or genes, receives its own embedding matrix, and products of these matrices yield interpretable loadings that expose interactions between the different dimensions.

What makes MANTRA technically distinctive is its Bayesian formulation with structured sparsity priors. The model places horseshoe priors on feature embeddings, a multi-scale shrinkage approach well suited to variational inference. Within this scheme, an Automatic Relevance Determination prior allows individual factors to be active in only a subset of data views, while local regularization encourages sparsity within each factor itself. This design has two practical consequences. First, unneeded factors are automatically driven toward zero, making the model remarkably robust when the true rank of the data is unknown, a common and frustrating problem in real applications. Second, the sparse factors highlight only the most relevant features, making the results biologically interpretable rather than opaque. Missing values, a perennial headache in clinical studies where not every omics layer can be profiled for every patient, are handled natively and in a principled manner.

The team validated MANTRA extensively on synthetic data before turning to real biology. In systematic benchmarks against PARAFAC, a state-of-the-art tensor decomposition implementation from the TensorLy package, MANTRA performed comparably in the high signal-to-noise regime and substantially better in the noisy, sparse, low-sample conditions that mimic real-world datasets. When the models were deliberately fitted with more factors than the true rank, MANTRA’s sparsity priors switched off the excess factors, whereas PARAFAC degraded. Scalability analyses on GPU hardware showed favorable scaling across sample counts, feature dimensions, and ranks, and sensitivity analyses confirmed that the choice of prior hyperparameters for the noise model leaves reconstruction accuracy stable across a broad range of data conditions.

The first real-world application focused on Chronic Lymphocytic Leukemia, a disease in which inter-patient heterogeneity strongly influences treatment outcomes. The researchers analyzed a published dataset of 192 primary CLL samples in which cell viability had been measured in response to 12 drugs under 17 different microenvironmental stimuli, complemented by bulk RNA sequencing of the same patients. This produced exactly the kind of mixed-order collection MANTRA was designed for: a third-order drug viability tensor of patients, drugs, and cytokines, alongside a second-order RNA-seq matrix of patients and genes. When trained on the drug tensor alone, MANTRA’s patient embeddings showed only a partial association with IGHV mutation status, one of the most important prognostic markers in CLL, distinguishing patients with typically aggressive unmutated disease from those with more indolent mutated disease.

The picture changed dramatically when the transcriptomic view was added. In the joint multi-view model, the patient embeddings separated sharply by IGHV status, and the drug loadings recovered known biological relationships, with drugs targeting the B-cell receptor, MAPK, and DNA damage response pathways clustering together. Quantitatively, the researchers used Leiden clustering of the learned latent space and measured alignment with clinical labels using adjusted Rand index and normalized mutual information, following standard practice from the single-cell integration literature. MANTRA outperformed MOFA+ and MOFA-FLEX, two leading matrix-based multi-omics tools, which had to flatten the three-dimensional drug tensor into stacks of two-dimensional matrices. MANTRA also separated patients by Trisomy 12, an intermediate-risk cytogenetic abnormality present in roughly ten to twenty percent of CLL patients, more accurately than the baselines, demonstrating that the model captures clinically meaningful axes of variation relevant to stratification and treatment response.

The second application pushed MANTRA into the single-cell arena, where the stakes were even higher. The team analyzed a multi-omics dataset from 18 pediatric patients with KMT2A-rearranged Acute Lymphoblastic Leukemia and 5 healthy donors, constructing two third-order tensors of patients, cell types, and features: one for single-cell RNA sequencing and one for single-cell ATAC sequencing. Because MANTRA tolerates missing values, it could use all 18 patients, whereas the specialized tool scITD, which requires every cell type to be observed in every donor, had to discard 7 of them. Both methods separated healthy donors from leukemia patients, but only MANTRA went further, splitting the patients into two distinct subgroups driven by a factor that was predominantly active in plasmacytoid dendritic cells, a rare immune cell population that turned out to be the surprising driver of disease heterogeneity.

Pathway analysis revealed what this plasmacytoid dendritic cell factor meant biologically. Genes loading strongly on the factor were enriched for interferon signaling and other immune-active pathways as well as endoplasmic reticulum stress programs, while lymphoid transcription factors such as ETV6 showed low loadings and genes typically implicated in T-cell lineage leukemia, including BCL2, MYC, and LYL1, showed high loadings. One patient subgroup carried a high-immune-activity, low-ER-stress program in their plasmacytoid dendritic cells, while the other occupied the opposite end of the spectrum. Critically, neither MOFA+, MOFA-FLEX, nor scITD detected this cell-type-specific stratification; all of their factors were dominated by blast cells. The finding was validated in an independent cohort of 7 pediatric B-ALL patients and 4 healthy donors, and when MANTRA was run on pediatric T-ALL data as a negative control, no such factor appeared, confirming that the plasmacytoid dendritic cell program is specific to B-cell acute lymphoblastic leukemia.

The linear structure of MANTRA is both its strength and its acknowledged limitation. Linear factor models are inherently interpretable, allowing biologists to trace each factor back to specific cell types, drugs, and pathways through the generalized loadings matrix. But capturing non-linear relationships would require kernel methods or deep architectures that would sacrifice precisely this transparency. The authors also note that in datasets where structural dependencies between dimensions are negligible, or where extreme sparsity and noise prevail, simpler matrix factorizations may remain equally effective or more stable. Identifiability and rotational invariance, perennial issues for all latent variable models, also apply here. Still, the researchers point toward supervised extensions of the framework as a promising future direction, albeit one that brings new overfitting challenges.

The implications reach well beyond leukemia. Drug screens that measure patient-derived cells across drugs and microenvironmental conditions, single-cell atlases that profile multiple tissues per donor, and multi-modal studies combining expression with chromatin accessibility all generate data with exactly the mixed-order tensor structure that MANTRA handles natively. By refusing to flatten higher-order structure into matrices, and by handling missing data through principled Bayesian inference rather than ad hoc imputation, the tool opens a window onto biological variation that existing methods systematically miss. The code is publicly available on GitHub, implemented in Python using the probabilistic programming library Pyro, and the discovery that a rare immune cell type defines clinically relevant leukemia subgroups offers a vivid demonstration of what becomes visible when algorithms finally learn to see data in all of its dimensions.

Subject of Research: Interpretable Bayesian integration of mixed-order multi-omics tensors for leukemia patient stratification

Article Title: Interpretable multi-omics integration across mixed-order tensors with MANTRA

Article References: De Azevedo, K., Oruc, Y. B., & Buettner, F. (2026). Interpretable multi-omics integration across mixed-order tensors with MANTRA. Molecular Systems Biology, 22(9), 1415-1429. https://doi.org/10.1038/s44320-026-00223-8

Image Credits: AI Generated

DOI: 10.1038/s44320-026-00223-8

Keywords: MANTRA, tensor decomposition, multi-omics, Bayesian inference, chronic lymphocytic leukemia, acute lymphoblastic leukemia, drug response, single-cell RNA-seq, single-cell ATAC-seq, plasmacytoid dendritic cells, structured sparsity, patient stratification