Identifying drift, diffusion, and causal structure from temporal snapshots

This Master thesis presents a comprehensive treatment of learning stochastic differential equations from temporal snapshots rather than complete trajectories.

Key Contributions:

• Establishes connections between trajectory inference and entropic optimal transport as a convex optimization problem
• Proves identifiability of drift and diffusion parameters under conditions excluding generalized rotational symmetries
• Demonstrates recovery of causal graphs from SDE parameters with additive diffusion
• Introduces APPEX (Alternating Projection Parameter Estimation from X0), an iterative algorithm for parameter estimation
• Validates the approach on simulated linear additive noise SDE data

Applications: Gene regulatory networks, contaminant transport modeling, financial markets, and image generation.

For a condensed version of this work, see the APPEX paper published on arXiv.

Recommended citation: Hossein Rahmani. (2025). "Identifying drift, diffusion, and causal structure from temporal snapshots." Master of Science Thesis, University of British Columbia. Supervised by Prof. Elina Robeva.