UVic Dynamics and Probability Seminar: Nitya Gadhiwala

Recent advances in single cell sequencing has led to the availability of gene expression data. We model the trajectories of cells in gene expression space using a diffusion and gradient drift process that also undergoes branching. In this talk, we show that one can recover the law of this process given time marginals using an entropy minimization problem. The optimization is over the set of all processes with the same branching mechanism and given marginals. We prove that among these the one which minimizes the relative entropy with respect to a reference branching Brownian motion is the ground truth. We conclude this talk with a general result showing that the solution to a entropy minimization problem with respect to a Markov reference measure with given marginals is also Markov.