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A scale-dependent notion of effective dimension

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arxiv 2001.10872 v1 pith:5VP3EGBO submitted 2020-01-29 stat.ML cs.LG

Oksana Berezniuk , Alessio Figalli , Raffaele Ghigliazza , Kharen Musaelian This is my paper · ORCID
classification stat.MLcs.LG
keywords dimensioneffectivenumberfisherinformationmatrixmodelnatural
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abstract

We introduce a notion of "effective dimension" of a statistical model based on the number of cubes of size $1/\sqrt{n}$ 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.

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