Learning Lineage-guided Geodesics with Finsler Geometry
This work addresses trajectory inference for applications like developmental biology, where incorporating lineage information is crucial, representing an incremental improvement over existing methods.
The paper tackles the problem of trajectory inference in dynamical systems by introducing a Finsler metric that integrates continuous geometric priors with discrete, directed prior knowledge, such as lineage trees, resulting in improved performance on interpolation tasks in synthetic and real-world data.
Trajectory inference investigates how to interpolate paths between observed timepoints of dynamical systems, such as temporally resolved population distributions, with the goal of inferring trajectories at unseen times and better understanding system dynamics. Previous work has focused on continuous geometric priors, utilizing data-dependent spatial features to define a Riemannian metric. In many applications, there exists discrete, directed prior knowledge over admissible transitions (e.g. lineage trees in developmental biology). We introduce a Finsler metric that combines geometry with classification and incorporate both types of priors in trajectory inference, yielding improved performance on interpolation tasks in synthetic and real-world data.