A scale-dependent notion of effective dimension

01/29/2020

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by   Oksana Berezniuk, et al.

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18

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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.