Abstract: Many high-dimensional biomedical datasets - including single cell gene expression profiles, medical images, and molecular structures - are naturally represented as probability distributions, histograms, or point clouds. To effectively analyze these data sources, we develop machine learning methods that operate directly in the space of probability measures. This space, while nonlinear and infinite-dimensional, admits a rich geometric structure that enables scalable and theoretically grounded learning algorithms.

In this talk, I will introduce computational tools for supervised, unsupervised, and manifold learning in the space of probability measures, with applications to omics and biomedical imaging datasets. These methods enable disease classification by leveraging the structure of data represented as probability distributions. I will also discuss temporal modeling approaches such as those based on stochastic gradient flows and trajectory inference with applications to analyzing single-cell exprssion profiles.