Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Concentration of solutions to random equations with concentration of measure hypotheses

Romain Couillet Cosme Louart 1, 2
1 LVIC - Laboratoire Vision et Ingénierie des Contenus
DIASI - Département Intelligence Ambiante et Systèmes Interactifs : DRT/LIST/DIASI
Abstract : We propose here to study the concentration of random objects that are implicitly formulated as fixed points to equations Y = f (X) where f is a random mapping. Starting from an hypothesis taken from the concentration of the measure theory, we are able to express precisely the concentration of such solutions, under some contractivity hypothesis on f. This statement has important implication to random matrix theory, and is at the basis of the study of some optimization procedures like the logistic regression for instance. In those last cases, we give precise estimations to the first statistics of the solution Y which allows us predict the performances of the algorithm.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [17 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02973851
Contributor : Cosme Louart <>
Submitted on : Wednesday, October 21, 2020 - 12:35:59 PM
Last modification on : Thursday, November 19, 2020 - 1:01:19 PM

File

2010.09877.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02973851, version 1

Collections

Citation

Romain Couillet, Cosme Louart. Concentration of solutions to random equations with concentration of measure hypotheses. 2020. ⟨hal-02973851⟩

Share

Metrics

Record views

27

Files downloads

39