Summary of Y-diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances, by Jannis Chemseddine et al.
Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances
by Jannis Chemseddine, Paul Hagemann, Christian Wald
First submitted to arxiv on: 20 Oct 2023
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Statistics Theory (math.ST); Machine Learning (stat.ML)
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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 introduces a new approach to inverse problems in conditional generative models, specifically targeting the Wasserstein distance. The authors propose a conditional Wasserstein distance that incorporates restricted couplings and prove its equivalence to the expected Wasserstein distance of posteriors. This leads to a novel loss function for Conditional Wasserstein GANs (CWGANs) and reveals conditions under which vanilla and conditional Wasserstein distances coincide. Numerical examples demonstrate the effectiveness of this approach in promoting favorable properties for posterior sampling. The paper’s methodology is rooted in the minimization of a distance between joint measures, but with a focus on controlling the Wasserstein distance rather than Kullback Leibler divergence. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about finding new ways to solve complex problems in machine learning. Imagine you have some data and want to generate more like it. This is called inverse problem. Many methods try to find the best solution by measuring how close they are to the true answer. But this approach doesn’t work well for all types of distances, especially Wasserstein distance. The authors introduce a new way to solve this problem using a special type of restricted couplings. They show that this method can be used to improve the performance of Conditional Wasserstein GANs (CWGANs) and provide examples to demonstrate its effectiveness. |
Keywords
* Artificial intelligence * Loss function * Machine learning
