Skip-Zeros Variational Inference in the Million-Cell Era of Single-Cell Transcriptomics

Abstract

Combinatorial indexing-based single-cell RNA sequencing methods such as sci-RNA-seq and sci-RNA-seq3 now enable the profiling of millions of cells, producing expression matrices that are both extremely sparse and high-dimensional. Conventional nonnegative matrix factorization (NMF) provides an interpretable framework for uncovering latent biological structures but is computationally prohibitive at this scale, as it requires explicit access to the vast number of zero entries. We introduce UNISON (Unified Sparse-Optimized Nonnegative factorization), a scalable framework for matrix and tensor factorization based on skip-zeros variational inference. By reformulating stochastic variational Bayes updates in terms of sufficient statistics, UNISON performs inference using only nonzero elements, while implicitly accounting for zeros through geometric sampling. This strategy enables efficient parameter estimation without matrix expansion and naturally accommodates multiple experimental contexts. Simulation studies show that UNISON is robust to diverse learning-rate schedules and mini-batch sizes, providing practical guidelines for optimization. Application to the Mouse Organogenesis Cell Atlas demonstrates scalability to over one million cells, yielding latent factors that capture developmental trajectories and lineage-specific signatures with improved interpretability compared to existing methods. Cross-species analysis of aqueous humor outflow pathways across five vertebrate species further highlights UNISONs ability to disentangle conserved from species-specific transcriptional programs and to recover biologically meaningful gene-gene and gene-phenotype relationships relevant to glaucoma. By efficiently exploiting sparsity while preserving interpretability, UNISON establishes a principled and practical solution for integrative, large-scale single-cell transcriptomics. Significance StatementSingle-cell technologies now generate datasets spanning millions of cells, creating massive, sparse matrices that are computationally difficult to analyze. Conventional methods often sacrifice statistical rigor for speed, either by discarding data or employing inappropriate models. We present UNISON, a framework that leverages a mathematical trick to perform exact inference using only nonzero elements. By combining this efficient computation with a probability model tailored for count data, UNISON scales to millions of cells while preserving information on rare cell types. This approach resolves the trade-off between scalability and accuracy, enabling precise integrative analyses of development and evolution across species without requiring massive computational resources.