Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots

Summary

The paper presents a method for jointly identifying the drift and diffusion of a stochastic differential equation (SDE) from its temporal marginals alone, without observing individual trajectories. Under linear drift and additive diffusion, non-identifiability arises only if the initial distribution has generalized rotational symmetries, and the authors prove that drift and diffusion can almost always be recovered otherwise. They also show the causal graph can be recovered from the identified parameters, and validate their iterative algorithm APPEX on simulated linear additive noise SDE data.