Extensions of independent component analysis: towards applications.

In practice, the application and extension of the ICA model depend on the problem and the data to be investigated. We finally focus on GARCH models in finance, and show that estimation of univariate or multivariate GARCH models is actually a nonlinear ICA problem; maximizing the likelihood is equiva...

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Other Authors: Zhang, Kun
Format: Others
Language:English
Chinese
Published: 2005
Subjects:
Online Access:http://library.cuhk.edu.hk/record=b6074028
http://repository.lib.cuhk.edu.hk/en/item/cuhk-343657
id ndltd-cuhk.edu.hk-oai-cuhk-dr-cuhk_343657
record_format oai_dc
collection NDLTD
language English
Chinese
format Others
sources NDLTD
topic Gaussian processes
Multivariate analysis
Neural networks (Computer science)
Signal processing--Digital techniques
spellingShingle Gaussian processes
Multivariate analysis
Neural networks (Computer science)
Signal processing--Digital techniques
Extensions of independent component analysis: towards applications.
description In practice, the application and extension of the ICA model depend on the problem and the data to be investigated. We finally focus on GARCH models in finance, and show that estimation of univariate or multivariate GARCH models is actually a nonlinear ICA problem; maximizing the likelihood is equivalent to minimizing the statistical dependence in standardized residuals. ICA can then be used for factor extraction in multivariate factor GARCH models. We also develop some extensions of ICA for this task. These techniques for extracting factors from multivariate return series are compared both theoretically and experimentally. We find that the one based on conditional decorrelation between factors behaves best. === In this thesis, first we consider the problem of source separation of post-nonlinear (PNL) mixtures, which is an extension of ICA to the nonlinear mixing case. With a large number of parameters, existing methods are computation-demanding and may be prone to local optima. Based on the fact that linear mixtures of independent variables tend to be Gaussian, we develop a simple and efficient method for this problem, namely extended Gaussianization. With Gaussianization as preprocessing, this method approximates each linear mixture of independent sources by the Cornish-Fisher expansion with only two parameters. Inspired by the relationship between the PNL mixing model and the Wiener system, extended Gaussianization is also proposed for blind inversion of Wiener systems. === Independent component analysis (ICA) is a recent and powerful technique for recovering latent independent sources given only their mixtures. The basic ICA model assumes that sources are linearly mixed and mutually independent. === Next, we study the subband decomposition ICA (SDICA) model, which extends the basic ICA model to allow dependence between sources by assuming that only some narrow-band source sub-components are independent. In SDICA, it is difficult to determine the subbands of source independent sub-components. We discuss the feasibility of performing SDICA in an adaptive manner. An adaptive method, called band selective ICA, is then proposed for this task. We also investigate the relationship between overcomplete ICA and SDICA and show that band selective ICA can solve the overcomplete ICA problems with sources having specific frequency localizations. Experimental results on separating images of human faces as well as artificial data are presented to verify the powerfulness of band selective ICA. === Zhang Kun. === "July 2005." === Adviser: Lai-Wan Chan. === Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3925. === Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. === Includes bibliographical references (p. 218-234). === Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Abstract in English and Chinese. === School code: 1307.
author2 Zhang, Kun
author_facet Zhang, Kun
title Extensions of independent component analysis: towards applications.
title_short Extensions of independent component analysis: towards applications.
title_full Extensions of independent component analysis: towards applications.
title_fullStr Extensions of independent component analysis: towards applications.
title_full_unstemmed Extensions of independent component analysis: towards applications.
title_sort extensions of independent component analysis: towards applications.
publishDate 2005
url http://library.cuhk.edu.hk/record=b6074028
http://repository.lib.cuhk.edu.hk/en/item/cuhk-343657
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spelling ndltd-cuhk.edu.hk-oai-cuhk-dr-cuhk_3436572019-02-19T03:41:24Z Extensions of independent component analysis: towards applications. CUHK electronic theses & dissertations collection Gaussian processes Multivariate analysis Neural networks (Computer science) Signal processing--Digital techniques In practice, the application and extension of the ICA model depend on the problem and the data to be investigated. We finally focus on GARCH models in finance, and show that estimation of univariate or multivariate GARCH models is actually a nonlinear ICA problem; maximizing the likelihood is equivalent to minimizing the statistical dependence in standardized residuals. ICA can then be used for factor extraction in multivariate factor GARCH models. We also develop some extensions of ICA for this task. These techniques for extracting factors from multivariate return series are compared both theoretically and experimentally. We find that the one based on conditional decorrelation between factors behaves best. In this thesis, first we consider the problem of source separation of post-nonlinear (PNL) mixtures, which is an extension of ICA to the nonlinear mixing case. With a large number of parameters, existing methods are computation-demanding and may be prone to local optima. Based on the fact that linear mixtures of independent variables tend to be Gaussian, we develop a simple and efficient method for this problem, namely extended Gaussianization. With Gaussianization as preprocessing, this method approximates each linear mixture of independent sources by the Cornish-Fisher expansion with only two parameters. Inspired by the relationship between the PNL mixing model and the Wiener system, extended Gaussianization is also proposed for blind inversion of Wiener systems. Independent component analysis (ICA) is a recent and powerful technique for recovering latent independent sources given only their mixtures. The basic ICA model assumes that sources are linearly mixed and mutually independent. Next, we study the subband decomposition ICA (SDICA) model, which extends the basic ICA model to allow dependence between sources by assuming that only some narrow-band source sub-components are independent. In SDICA, it is difficult to determine the subbands of source independent sub-components. We discuss the feasibility of performing SDICA in an adaptive manner. An adaptive method, called band selective ICA, is then proposed for this task. We also investigate the relationship between overcomplete ICA and SDICA and show that band selective ICA can solve the overcomplete ICA problems with sources having specific frequency localizations. Experimental results on separating images of human faces as well as artificial data are presented to verify the powerfulness of band selective ICA. Zhang Kun. "July 2005." Adviser: Lai-Wan Chan. Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3925. Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. Includes bibliographical references (p. 218-234). Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. Abstract in English and Chinese. School code: 1307. Zhang, Kun Chinese University of Hong Kong Graduate School. Division of Computer Science and Engineering. 2005 Text theses electronic resource microform microfiche 1 online resource (xx, 234 p. : ill.) cuhk:343657 isbn: 9780542760396 http://library.cuhk.edu.hk/record=b6074028 eng chi Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) http://repository.lib.cuhk.edu.hk/en/islandora/object/cuhk%3A343657/datastream/TN/view/Extensions%20of%20independent%20component%20analysis%20%3A%20towards%20applications.jpghttp://repository.lib.cuhk.edu.hk/en/item/cuhk-343657