Summary of Theoretical Guarantees For Variational Inference with Fixed-variance Mixture Of Gaussians, by Tom Huix et al.
Theoretical Guarantees for Variational Inference with Fixed-Variance Mixture of Gaussians
by Tom Huix, Anna Korba, Alain Durmus, Eric Moulines
First submitted to arxiv on: 6 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 investigates the theoretical properties of Variational Inference (VI) in non-Gaussian cases, specifically focusing on Mixture of Gaussians with fixed covariance and constant weights. The authors cast VI as the minimization of a mollified relative entropy, where the support of an atomic measure corresponds to the localization of Gaussian components. They propose solving VI by optimizing the positions of Diracs (particles) through gradient descent, which takes the form of an interacting particle system. The paper studies two sources of error in VI: optimization results and approximation errors. By establishing a descent lemma and upper bounding the objective between an optimal finite mixture and the target distribution, the authors provide insights into the theoretical properties of VI. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper explores how to improve Variational Inference (VI) when working with complex data distributions that aren’t just Gaussians. They focus on a specific type of complex distribution called Mixture of Gaussians. The idea is to minimize a special kind of distance between the target distribution and a simpler distribution that’s easy to work with. To do this, they treat each Gaussian component as a “particle” that can move around to find the best fit. They show how to use gradient descent to optimize these particles’ positions, which leads to insights into why VI works or doesn’t work well in different situations. |
Keywords
» Artificial intelligence » Gradient descent » Inference » Optimization
