Hierarchical Weak Supervision for Multilevel Representation Learning with scPACE

Scientific and clinical datasets often consist of groups of exchangeable instances, such as thousands of cells sampled from a patient or donor. Yet information is distributed unevenly across these levels: integer-valued molecular counts are measured for individual cells, whereas phenotypes such as age, diagnosis, or disease severity are typically measured only for the donor. Cell-level phenotypes and cell-type labels may be sparse or missing. Although modern generative models can represent single-cell count data, they do not typically model how donor-level biological variation manifests through cellular states, cell-type composition, and gene expression. We introduce scPACE, a hierarchical generative model that represents each donor by an underlying biological state and each cell by its position along a related biological continuum, such as developmental pseudotime, cellular maturity, or disease-associated progression. This structure explicitly captures how donor-level variation is expressed heterogeneously across individual cells. Under explicit assumptions, the latent state hierarchy is identifiable up to a sign convention. We apply scPACE to large-scale real-world single-cell studies spanning mouse cortical development, and Alzheimer’s and Huntington’s disease. Our framework provides a principled foundation for generative modeling of phenotype-linked biological variation across donors and cells, enabling the study of developmental and disease progression across biological scales.