Mathematics Colloquia and Seminars

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Description

Biological and biomedical datasets often contain many correlated measurements while reliable phenotype labels are available for only a subset of observations. This occurs in single-cell data, where confidently annotated cell identities may be limited; drug-response studies, where molecular profiles are more readily available than experimental responses; and clinical studies, where outcomes require follow-up or expert adjudication. With limited labels, supervised methods can overfit or select only a few among correlated predictors. Yet correlation can also be informative, as related measurements may provide complementary or redundant descriptions of the same phenotype. Even without labels, the density and distribution of observations reveal which measurements commonly occur together and which observations are similar. Unsupervised methods exploit this organization but cannot necessarily direct it toward a class or phenotype of interest. Semi-supervised learning bridges these approaches: labels define what is predicted, while the entire dataset reveals how the data are organized. We developed the Path-Likelihood Algorithm (PLA), a semi-supervised method based on the hypothesis that observations with similar phenotypes can be represented such that they lie close to one another. PLA constructs local relationships and simulates random walks from observations with known labels. These walks propagate through labeled and unlabeled neighbors and preferentially accumulate among observations with the same phenotype. PLA uses the likelihood of paths connecting observations to members of different labeled classes to determine class probabilities, reducing a complex network to a simpler probabilistic description of each class. PLA learns combinations of measured variables that maximize classification accuracy among labeled observations. Importantly, unlabeled observations act as bridges along random-walk paths and therefore influence learning. Thus, sparse labels identify phenotype-relevant relationships, while the entire dataset determines how observations are connected. PLA achieved high accuracy with very few labels while remaining computationally efficient. On Levine32, a 32-marker mass-cytometry dataset of ~100,000 human bone-marrow cells representing 14 cell types, PLA achieved 0.97 accuracy using only 140 cells for training (10 per cell type) and the remaining cells for evaluation. We further tested PLA in 1,019 patients with myocardial infarction. These results demonstrate the potential of PLA for classification when reliable labels are scarce.