Summary of Convergence Of Coordinate Ascent Variational Inference For Log-concave Measures Via Optimal Transport, by Manuel Arnese and Daniel Lacker
Convergence of coordinate ascent variational inference for log-concave measures via optimal transport
by Manuel Arnese, Daniel Lacker
First submitted to arxiv on: 12 Apr 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR); Statistics Theory (math.ST)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper focuses on mean field variational inference (VI), a method for approximating high-dimensional probability measures by finding the closest product measure. The Coordinate Ascent Variational Inference (CAVI) algorithm is widely used, but its convergence properties are not well understood. This study proves the convergence of CAVI for log-concave densities and provides rate of convergence results under additional assumptions. The analysis relies on the displacement convexity of mean field VI when the target density is log-concave, which allows adaptation of techniques from Euclidean space optimization literature. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper solves a tricky math problem called “mean field variational inference”. It’s like trying to find the closest approximation of a complex probability measure. The researchers study an algorithm called CAVI that’s used a lot, but nobody knows how it converges. They prove that CAVI works for certain types of density and show how fast it gets closer to the true answer. |
Keywords
* Artificial intelligence * Inference * Optimization * Probability
