# A scale-dependent notion of effective dimension

arXiv: https://arxiv.org/abs/2001.10872 · HTML: https://mlsanity.com/paper/2001.10872/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2020.

## Built on by (most cited first, 17 of 17)

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## Abstract (arXiv)

We introduce a notion of "effective dimension" of a statistical model based on the number of cubes of size 1/√n needed to cover the model space when endowed with the Fisher Information Matrix as metric, n being the number of observations. The number of observations fixes a natural scale or resolution. The effective dimension is then measured via the spectrum of the Fisher Information Matrix regularized using this natural scale.