Summary of Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation For the Square Loss, by Ingvar Ziemann et al.
Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Loss
by Ingvar Ziemann, Stephen Tu, George J. Pappas, Nikolai Matni
First submitted to arxiv on: 8 Feb 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 This paper investigates statistical learning with dependent data using square loss in a hypothesis class. The study aims to identify a sharp noise interaction term, or variance proxy, in learning with dependent data. Without making any realizability assumptions, the authors show that the empirical risk minimizer achieves a rate that only depends on the complexity of the class and second-order statistics in its leading term. This result holds regardless of whether the problem is realizable or not, and is referred to as a “near mixing-free rate”. The authors combine the notion of a weakly sub-Gaussian class with mixed tail generic chaining to compute sharp rates for various problems, including sub-Gaussian linear regression, smoothly parameterized function classes, finite hypothesis classes, and bounded smoothness classes. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how we can learn from data that is connected or dependent. The goal is to find a way to measure the noise in this kind of data. Without making any big assumptions about what we’re trying to learn, the authors show that we can get good results by looking only at the complexity of the thing we’re learning and some statistics from the data. This works whether the problem is easy or hard, and it’s called a “near mixing-free rate”. The authors use two ideas together – one about classes of functions and another about how to combine them – to come up with a way to get good results for many different kinds of problems. |
Keywords
* Artificial intelligence * Linear regression
