Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Prior

arXiv:2406.07475v1 Announce Type: new
Abstract: Trajectory inference seeks to recover the temporal dynamics of a population from snapshots of its (uncoupled) temporal marginals, i.e. where observed particles are not tracked over time. Lavenant et al. arXiv:2102.09204 addressed this challenging problem under a stochastic differential equation (SDE) model with a gradient-driven drift in the observed space, introducing a minimum entropy estimator relative to the Wiener measure. Chizat et al. arXiv:2205.07146 then provided a practical grid-free mean-field Langevin (MFL) algorithm using Schr\"odinger …

abstract arxiv cs.lg differential differential equation dynamics equation inference population prior problem snapshots stat.ml stochastic temporal trajectory transport type