Summary of Identifying Drift, Diffusion, and Causal Structure From Temporal Snapshots, by Vincent Guan et al.
Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots
by Vincent Guan, Joseph Janssen, Hossein Rahmani, Andrew Warren, Stephen Zhang, Elina Robeva, Geoffrey Schiebinger
First submitted to arxiv on: 30 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper presents a comprehensive approach for identifying the drift and diffusion of stochastic differential equations (SDEs) from their temporal marginals. The approach is motivated by the increasing availability of single-cell datasets and assumes linear drift and additive diffusion. The authors prove that these parameters are identifiable from marginals if the initial distribution lacks any generalized rotational symmetries. Additionally, they show that the causal graph of an SDE with additive diffusion can be recovered from its parameters. To handle anisotropic diffusion, the authors adapt entropy-regularized optimal transport and introduce APPEX (Alternating Projection Parameter Estimation from X0), an iterative algorithm for estimating the drift, diffusion, and causal graph of an additive noise SDE. APPEX is shown to iteratively decrease Kullback-Leibler divergence to the true solution. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper solves a challenging problem in machine learning by developing a new approach for identifying stochastic differential equations (SDEs) from their temporal marginals. This can be used to model dynamic processes like gene regulatory networks, financial markets, and image generation. The approach is based on linear drift and additive diffusion assumptions and is motivated by the increasing availability of single-cell datasets. |
Keywords
» Artificial intelligence » Diffusion » Image generation » Machine learning
