Nonlinear Independent Component Analysis: Theoretical Review And Applications

Filho, Eduardo Furtado Simas; Seixas, J. M.

doi:10.21528/lnlm-vol5-no2-art3

Cited by 2 publications

(2 citation statements)

References 78 publications

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“…By imposing some constraints on the nonlinear mixing mapping or the independent components ( , the independent components ( can be properly estimated. See Simas Filho and Seixas [8] for an overview of the main statistical principles and some algorithms for estimating the independent components. For simplicity, in this paper we suppose that…”

Section: Multistep-adjustment By Correlationmentioning

confidence: 99%

Remodeling and Estimation for Sparse Partially Linear Regression Models

Zeng

Wang

Lin

2013

Abstract and Applied Analysis

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When the dimension of covariates in the regression model is high, one usually uses a submodel as a working model that contains significant variables. But it may be highly biased and the resulting estimator of the parameter of interest may be very poor when the coefficients of removed variables are not exactly zero. In this paper, based on the selected submodel, we introduce a two-stage remodeling method to get the consistent estimator for the parameter of interest. More precisely, in the first stage, by a multistep adjustment, we reconstruct an unbiased model based on the correlation information between the covariates; in the second stage, we further reduce the adjusted model by a semiparametric variable selection method and get a new estimator of the parameter of interest simultaneously. Its convergence rate and asymptotic normality are also obtained. The simulation results further illustrate that the new estimator outperforms those obtained by the submodel and the full model in the sense of mean square errors of point estimation and mean square prediction errors of model prediction.

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Section: Multistep-adjustment By Correlationmentioning

confidence: 99%

Remodeling and Estimation for Sparse Partially Linear Regression Models

Zeng

Wang

Lin

2013

Abstract and Applied Analysis

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“…NLICA algorithms have been recently applied in different problems such as speech processing [76] and image denoising [77]. A complete review on nonlinear ICA/BSS theory, algorithms and applications can be found in [78].…”

Section: 2-nonlinear Ica/bssmentioning

confidence: 99%

Independent Component Analysis and Blind Signal Separation: Theory, Algorithms and Applications

Filho¹,

Seixas²,

Moura³

et al. 2012

L&NLM

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This paper reviews Independent Components Analysis (ICA) and Blind Signal Separation (BSS) problems. An overview on the main statistical principles that guide the search for the independent components is formulated, methods for blind signal separation that require both high-order and second-order statistics are also illustrated. Some of the most successful algorithms for both ICA and BSS are derived. Experimental applications in different signal processing tasks such as passive sonar, nondestructive ultrasound inspection and electrical-load time series are presented.

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Nonlinear Independent Component Analysis: Theoretical Review And Applications

Cited by 2 publications

References 78 publications

Remodeling and Estimation for Sparse Partially Linear Regression Models

Remodeling and Estimation for Sparse Partially Linear Regression Models

Independent Component Analysis and Blind Signal Separation: Theory, Algorithms and Applications

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