Summary of Stochastic Inverse Problem: Stability, Regularization and Wasserstein Gradient Flow, by Qin Li et al.
Stochastic Inverse Problem: stability, regularization and Wasserstein gradient flow
by Qin Li, Maria Oprea, Li Wang, Yunan Yang
First submitted to arxiv on: 30 Sep 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR)
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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 explores stochastic inverse problems in physical or biological sciences, where an unknown parameter’s probability distribution is sought to produce data aligned with measurements. It investigates three aspects: direct inversion, variational formulation with regularization, and optimization via gradient flows, drawing parallels with deterministic inverse problems. The key difference lies in operating within a probability space rather than Euclidean or Sobolev spaces, necessitating tools from measure transport theory. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at ways to solve a type of problem where we don’t know what’s causing some measurements, and we want to figure out the probability that it might be one thing or another. It compares three different approaches to solving this kind of problem: trying to invert the process directly, adding constraints to make the solution more stable, and finding the best solution by adjusting variables in a special way. The big difference is that instead of working with numbers like we usually do, we’re working with probabilities, which requires some new tools. |
Keywords
» Artificial intelligence » Optimization » Probability » Regularization
