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Description
  • Studujeme minimalizaci regularizovaného funkcionálu empirické chyby se stabilizátorem založeným na Fourierově transformaci. Dokážeme existenci a jednoznačnost řešení. Dále popíšeme tvar minimalizující funkce a ukážeme, že je ve tvaru dopředné neuronové sítě s jednou skrytou vrstvou a aktivačními funkcemi odvozenými od regularizační části. Praktické aplikace založené na této myšlence byly studovány a bylo ukázáno, že nejlépe pracují pro úlohy s nižší vstupní dimenzí nebo odpovídající konceptuální charakteristikou (např. finanční aplikace nebo klasifikace obrazu). (cs)
  • We study minimization of regularized empirical error functional with a Fourier-based stabilizer. We prove existence and uniqueness of the solution. We also describe the shape of the minimizing function and show that it is in the form of a one-hidden layer feed-forward neural network with activation functions derived from the regularization part. Practical applications based on the idea have been studied performing best on tasks with lower input dimension or suitable conceptual characteristics (e.g. financial fields or image classification).
  • We study minimization of regularized empirical error functional with a Fourier-based stabilizer. We prove existence and uniqueness of the solution. We also describe the shape of the minimizing function and show that it is in the form of a one-hidden layer feed-forward neural network with activation functions derived from the regularization part. Practical applications based on the idea have been studied performing best on tasks with lower input dimension or suitable conceptual characteristics (e.g. financial fields or image classification). (en)
Title
  • Existence and Uniqueness of Minimization Problems with Fourier Based Stabilizers
  • Existence and Uniqueness of Minimization Problems with Fourier Based Stabilizers (en)
  • Existence a jednoznačnost milimalizačních problémů s Fourierovským stabilizátorem (cs)
skos:prefLabel
  • Existence and Uniqueness of Minimization Problems with Fourier Based Stabilizers
  • Existence and Uniqueness of Minimization Problems with Fourier Based Stabilizers (en)
  • Existence a jednoznačnost milimalizačních problémů s Fourierovským stabilizátorem (cs)
skos:notation
  • RIV/67985807:_____/04:00105194!RIV/2005/AV0/A06005/N
http://linked.open.../vavai/riv/strany
  • 1853;1860
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/02/0428), Z(AV0Z1030915)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 563602
http://linked.open...ai/riv/idVysledku
  • RIV/67985807:_____/04:00105194
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • neural networks; minimization of functionals; regularization theory; stabilizers; Fourier transform (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [965DB594CFF4]
http://linked.open...v/mistoKonaniAkce
  • Prague
http://linked.open...i/riv/mistoVydani
  • Heidelberg
http://linked.open...i/riv/nazevZdroje
  • Computational Statistics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Šidlofová, Terezie
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
number of pages
http://purl.org/ne...btex#hasPublisher
  • Physica Verlag
https://schema.org/isbn
  • 3-7908-1554-3
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