Summary of Convergence Of Statistical Estimators Via Mutual Information Bounds, by El Mahdi Khribch et al.
Convergence of Statistical Estimators via Mutual Information Bounds
by El Mahdi Khribch, Pierre Alquier
First submitted to arxiv on: 24 Dec 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); 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 introduces a novel mutual information bound for statistical models, which has far-reaching applications in statistical inference. The derived bound improves contraction rates for fractional posteriors in Bayesian nonparametrics and can be used to analyze various estimation methods like variational inference or Maximum Likelihood Estimation (MLE). By bridging diverse areas of research, this work advances our understanding of the fundamental limits of statistical inference and the role of information in learning from data. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about a new way to understand how well we can learn from data. It connects three important ideas: mutual information, PAC-Bayesian theory, and Bayesian nonparametrics. This connection helps us better understand how we can use data to make predictions or estimate things. The new idea has many uses, like improving how we do statistical analysis or learning about different types of statistical methods. |
Keywords
* Artificial intelligence * Inference * Likelihood
