# `local' vs. `global' parameters -- breaking the gaussian complexity barrier

arXiv: https://arxiv.org/abs/1504.02191 · HTML: https://mlsanity.com/paper/1504.02191/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2015.

## Built on by (most cited first, 2 of 2)

- [Minimax Linear Regression under the Quantile Risk](https://mlsanity.com/paper/2406.12145/) (2024)
- [Do we really need the Rademacher complexities?](https://mlsanity.com/paper/2502.15118/) (2025)

## Abstract (arXiv)

We show that if F is a convex class of functions that is L-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower estimates on the error rate for such problems.