Summary of How to Shrink Confidence Sets For Many Equivalent Discrete Distributions?, by Odalric-ambrym Maillard and Mohammad Sadegh Talebi
How to Shrink Confidence Sets for Many Equivalent Discrete Distributions?
by Odalric-Ambrym Maillard, Mohammad Sadegh Talebi
First submitted to arxiv on: 22 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Systems and Control (eess.SY)
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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 We present a strategy to refine high-probability confidence sets for discrete distributions, leveraging permutation-equivalence. This property arises when each distribution is obtained from a common unknown distribution via an unknown permutation. Our approach exploits this structure to improve confidence set sizes. We provide finite-time bounds on the refined confidence sets and establish conditions under which our method outperforms individual confidence sets. Our result implies asymptotic rate improvements for elements inside and outside the support of the underlying distribution. This work has implications for machine learning problems, such as reinforcement learning tasks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine you have a set of unknown patterns or distributions, and you can build a good estimate of each one based on some data. Now, what if these patterns are related in a special way? That’s the idea behind permutation-equivalence. It means that each pattern is obtained from another common pattern by applying an unknown mix-up to the same alphabet. Our goal is to use this relationship to improve our estimates. We show how to do this and provide guarantees on the quality of our improved estimates. This work has practical applications in areas like machine learning. |
Keywords
» Artificial intelligence » Machine learning » Probability » Reinforcement learning
