Charlotte Bunne, head of EPFL's Artificial Intelligence in Molecular Medicine Group, is developing AI algorithms to better understand the incredibly complex and high-dimensional data that represent the hundreds of tissue layers and protein markers in an individual cell. EPFL magazine Dimensions spoke to Charlotte Bunne about her work at the cutting-edge of AI in medicine and biology. Could you describe the focus of your research? We are developing diagnostic tools for clinics that are driven by AI technologies. This includes forecasting the best treatment that a patient should receive, trying to understand the state of disease that a patient is in, and deciphering important biomarkers or potential drug targets that we should investigate further.

The static optimal transport $(\mathrm{OT})$ problem between Gaussians seeks to recover an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been well studied and applied to a wide variety of tasks. Here we focus on the dynamic formulation of OT, also known as the Schr\"odinger bridge (SB) problem, which has recently seen a surge of interest in machine learning due to its connections with diffusion-based generative models. In contrast to the static setting, much less is known about the dynamic setting, even for Gaussian distributions. In this paper, we provide closed-form expressions for SBs between Gaussian measures. In contrast to the static Gaussian OT problem, which can be simply reduced to studying convex programs, our framework for solving SBs requires significantly more involved tools such as Riemannian geometry and generator theory. Notably, we establish that the solutions of SBs between Gaussian measures are themselves Gaussian processes with explicit mean and covariance kernels, and thus are readily amenable for many downstream applications such as generative modeling or interpolation. To demonstrate the utility, we devise a new method for modeling the evolution of single-cell genomics data and report significantly improved numerical stability compared to existing SB-based approaches.