Summary of Conditional Wasserstein Distances with Applications in Bayesian Ot Flow Matching, by Jannis Chemseddine et al.
Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching
by Jannis Chemseddine, Paul Hagemann, Gabriele Steidl, Christian Wald
First submitted to arxiv on: 27 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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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 A novel approach is introduced in this paper to address challenges in inverse problems. Traditional methods use generative models to approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. However, these methods do not guarantee control over the distance between posterior measures when using the Wasserstein distance. To overcome this limitation, the authors propose a conditional Wasserstein distance via restricted couplings, which equals the expected Wasserstein distance of posteriors. The dual formulation of this distance is shown to resemble losses in conditional Wasserstein GAN literature. Theoretical properties are derived, and geodesics, velocity fields, and flow ODEs are characterized. To improve velocity field approximations, the authors propose relaxing the conditional Wasserstein distance. This leads to an extension of OT Flow Matching for solving Bayesian inverse problems, which is demonstrated numerically on an inverse problem and class-conditional image generation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper solves a big problem in computer science called inverse problems. Imagine trying to figure out what’s inside a black box just by looking at how it works from the outside. That’s basically what inverse problems are all about. The tricky part is that most methods used to solve these problems don’t work well with certain types of data. To fix this, the authors came up with a new way to measure how different two things are (like how close a guess is to the real answer). This new method helps solve inverse problems and even creates realistic images from given conditions. |
Keywords
* Artificial intelligence * Gan * Image generation
