Optimal transport and stochastic processes in developmental biology

Abstract

Optimal transport is a rapidly growing area of research at the intersection of probability, analysis, and optimization. It gives rise to powerful tools for comparing probability distributions and computing couplings between random variables, and it has found applications in physics, economics, statistics, machine learning and biology.

This minicourse introduces the powerful computational and analytical tools of optimal transport and demonstrates how these concepts can be applied to analyze stochastic processes in biomedical data science. In addition to a self-contained introduction to the classical theory and the modern developments, we explain how concepts from optimal transport can be applied to model a developing population of cells as a curve in the space of probability distributions. We highlight new experimental technologies, like single cell RNA sequencing, that allow us to sample from these probability distributions, and we show how to use optimal transport to recover a developmental curve from samples at various time-points. We illustrate these concepts with an interactive tutorial, using real data from stem cell reprogramming.

There will be two main speakers of this minicourse, Hugo Lavenant and Geoffrey Schiebinger.

No knowledge of biology or optimal transport will be required. Familiarity with elementary concepts in probability theory and optimization might be helpful.

Brendan Pass

Associate Professor

Young-Heon Kim

Professor