Summary of Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimization, by Xu Cai and Jonathan Scarlett
Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimization
by Xu Cai, Jonathan Scarlett
First submitted to arxiv on: 11 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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 The paper presents an investigation into estimating the normalizing constant in reproducing kernel Hilbert spaces (RKHS) through queries to black-box functions. The authors demonstrate that the difficulty level of this problem depends on a parameter lambda, with small values resulting in Bayesian quadrature and large values yielding Bayesian optimization. The study also explores the impact of noisy function evaluations, providing both algorithm-independent lower bounds and upper bounds, as well as simulation results across various benchmark functions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper tries to figure out how to estimate something called a normalizing constant using special math tools called reproducing kernel Hilbert spaces. They find that it’s easier or harder depending on how big the number lambda is. When lambda is small, it’s like trying to solve one problem, and when it’s really big, it’s like solving another problem. The authors also test their ideas with noisy data and show that their results make sense. |
Keywords
* Artificial intelligence * Optimization
