Learning the Right Model from the Data
In this chapter we discuss the problem of finding the shift-invariant space model that best fits a given class of observed data F. If the data is known to belong to a fixed—but unknown—shift-invariant space V(Φ) generated by a vector function Φ, then we can probe the data F to find out whether the d...
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2006
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Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_22965009_v_n9780817637781_p325_Aldroubi http://hdl.handle.net/20.500.12110/paper_22965009_v_n9780817637781_p325_Aldroubi |
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paper:paper_22965009_v_n9780817637781_p325_Aldroubi2023-06-08T16:35:26Z Learning the Right Model from the Data Class Versus Optimal Space Orthonormal Basis Riesz Basis Space Versus In this chapter we discuss the problem of finding the shift-invariant space model that best fits a given class of observed data F. If the data is known to belong to a fixed—but unknown—shift-invariant space V(Φ) generated by a vector function Φ, then we can probe the data F to find out whether the data is sufficiently rich for determining the shift-invariant space. If it is determined that the data is not sufficient to find the underlying shift-invariant space V, then we need to acquire more data. If we cannot acquire more data, then instead we can determine a shift-invariant subspace S ⊂ V whose elements are generated by the data. For the case where the observed data is corrupted by noise, or the data does not belong to a shift-invariant space V(Φ), then we can determine a space V(Φ) that fits the data in some optimal way. This latter case is more realistic and can be useful in applications, e.g., finding a shift-invariant space with a small number of generators that describes the class of chest X-rays. © 2006, Birkhäuser Boston. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_22965009_v_n9780817637781_p325_Aldroubi http://hdl.handle.net/20.500.12110/paper_22965009_v_n9780817637781_p325_Aldroubi |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Class Versus Optimal Space Orthonormal Basis Riesz Basis Space Versus |
spellingShingle |
Class Versus Optimal Space Orthonormal Basis Riesz Basis Space Versus Learning the Right Model from the Data |
topic_facet |
Class Versus Optimal Space Orthonormal Basis Riesz Basis Space Versus |
description |
In this chapter we discuss the problem of finding the shift-invariant space model that best fits a given class of observed data F. If the data is known to belong to a fixed—but unknown—shift-invariant space V(Φ) generated by a vector function Φ, then we can probe the data F to find out whether the data is sufficiently rich for determining the shift-invariant space. If it is determined that the data is not sufficient to find the underlying shift-invariant space V, then we need to acquire more data. If we cannot acquire more data, then instead we can determine a shift-invariant subspace S ⊂ V whose elements are generated by the data. For the case where the observed data is corrupted by noise, or the data does not belong to a shift-invariant space V(Φ), then we can determine a space V(Φ) that fits the data in some optimal way. This latter case is more realistic and can be useful in applications, e.g., finding a shift-invariant space with a small number of generators that describes the class of chest X-rays. © 2006, Birkhäuser Boston. |
title |
Learning the Right Model from the Data |
title_short |
Learning the Right Model from the Data |
title_full |
Learning the Right Model from the Data |
title_fullStr |
Learning the Right Model from the Data |
title_full_unstemmed |
Learning the Right Model from the Data |
title_sort |
learning the right model from the data |
publishDate |
2006 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_22965009_v_n9780817637781_p325_Aldroubi http://hdl.handle.net/20.500.12110/paper_22965009_v_n9780817637781_p325_Aldroubi |
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1768544934267191296 |