Hossein Rahmani

Hossein Rahmani

Applied ML Scientist at TD | M.Sc. Applied Math (Causal Inference), UBC | CS, Sharif University of Technology

Publications

You can also find my articles on my Google Scholar profile.

Identifying drift, diffusion, and causal structure from temporal snapshots Permalink

Published in Master of Science Thesis, University of British Columbia, 2025

Master Thesis exploring the learning of stochastic differential equations from temporal marginal distributions. This work establishes connections between trajectory inference and entropic optimal transport, proves identifiability of drift and diffusion parameters, and demonstrates recovery of causal graphs from SDE parameters.

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.

Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots Permalink

Published in Arxiv, 2024

We present the first comprehensive approach for jointly estimating the drift and diffusion of an SDE from its temporal marginals. Assuming linear drift and additive diffusion, we prove that these parameters are identifiable from marginals if and only if the initial distribution is not invariant to a class of generalized rotations, a condition that is satisfied by most distributions. We further prove that the causal graph of any SDE with additive diffusion can be recovered from the SDE parameters. To complement this theory, we adapt entropy-regularized optimal transport to handle anisotropic diffusion, and introduce APPEX (Alternating Projection Parameter Estimation from X0), an iterative algorithm designed to estimate the drift, diffusion, and causal graph of an additive noise SDE, solely from temporal marginals.

Recommended citation: Vincent Guan, Joseph Janssen, Hossein Rahmani, Andrew Warren, Stephen Zhang, Elina Robeva, and Geoffrey Schiebinger. (2024). "Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots." arXiv:2410.22729.