Summary of Fast Convergence Of the Expectation Maximization Algorithm Under a Logarithmic Sobolev Inequality, by Rocco Caprio et al.
Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequality
by Rocco Caprio, Adam M Johansen
First submitted to arxiv on: 25 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC); Statistics Theory (math.ST); Computation (stat.CO)
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 builds upon recent advancements in constructing gradient flows on Wasserstein spaces to analyze the Expectation Maximization (EM) algorithm, which is commonly represented as coordinate-wise minimization on the product of a Euclidean space and a space of probability distributions. By extending an analysis technique used for alternating minimization algorithms on Euclidean space, the paper obtains finite sample error bounds and exponential convergence of the EM algorithm under a natural generalisation of a log-Sobolev inequality. Additionally, the authors demonstrate the flexibility of the analysis technique in analyzing several variants of the EM algorithm. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how a popular machine learning algorithm works better. The algorithm is called Expectation Maximization (EM), and it’s used to solve problems where you have some data but not enough information to make predictions. The authors use new math tools to analyze how well the EM algorithm does, and they show that it can work really well in certain situations. |
Keywords
* Artificial intelligence * Machine learning * Probability
