Wavelet-Based Weighted LASSO and Screening Approaches in Functional Linear Regression

Zhao, Yihong; Chen, Huaihou; Ogden, R. Todd

doi:10.1080/10618600.2014.925458

Cited by 39 publications

(29 citation statements)

References 36 publications

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“…Zhu, Vannucci and Cox, 2010). We note that this meta-algorithm has been applied before for 1D functional predictors (Brown, Fearn and Vannucci, 2001; Wang, Ray and Mallick, 2007; Malloy et al, 2010; Zhao, Ogden and Reiss, 2012), and more for image predictors (Wang et al, 2014; Zhao, Chen and Ogden, 2014). Past work on wavelet-domain classification, as opposed to regression (e.g.…”

Section: Wavelets and Their Use In Regression On Imagesmentioning

confidence: 99%

“…Since wavelet bases are well suited for sparse representation of functions, recent work has considered combining them with sparsity-inducing penalties, both for semiparametric regression (Wand and Ormerod, 2011) and for regression with functional or image predictors (Zhao, Ogden and Reiss, 2012; Wang et al, 2014; Zhao, Chen and Ogden, 2014). The latter papers focused on

ℓ_{1}

penalization, also known as the lasso (Tibshirani, 1996), in the wavelet domain.…”

Section: Three Wavelet-domain Algorithmsmentioning

confidence: 99%

See 1 more Smart Citation

Wavelet-domain regression and predictive inference in psychiatric neuroimaging

Reiss¹,

Huo²,

Zhao³

et al. 2015

Ann. Appl. Stat.

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An increasingly important goal of psychiatry is the use of brain imaging data to develop predictive models. Here we present two contributions to statistical methodology for this purpose. First, we propose and compare a set of wavelet-domain procedures for fitting generalized linear models with scalar responses and image predictors: sparse variants of principal component regression and of partial least squares, and the elastic net. Second, we consider assessing the contribution of image predictors over and above available scalar predictors, in particular via permutation tests and an extension of the idea of confounding to the case of functional or image predictors. Using the proposed methods, we assess whether maps of a spontaneous brain activity measure, derived from functional magnetic resonance imaging, can meaningfully predict presence or absence of attention deficit/hyperactivity disorder (ADHD). Our results shed light on the role of confounding in the surprising outcome of the recent ADHD-200 Global Competition, which challenged researchers to develop algorithms for automated image-based diagnosis of the disorder.

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Section: Wavelets and Their Use In Regression On Imagesmentioning

confidence: 99%

ℓ_{1}

penalization, also known as the lasso (Tibshirani, 1996), in the wavelet domain.…”

Section: Three Wavelet-domain Algorithmsmentioning

confidence: 99%

Wavelet-domain regression and predictive inference in psychiatric neuroimaging

Reiss¹,

Huo²,

Zhao³

et al. 2015

Ann. Appl. Stat.

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“…In order to provide a good approximation of the functional coefficients, a large number of basis should be chosen. However, this may cause overfitting of the model and to remedy that various penalty methods have been proposed [10,44]. The fPC method has been extensively studied [19,27] where the fPC of z i (t) serve as the basis.…”

Section: Introductionmentioning

confidence: 99%

Partial functional linear quantile regression for neuroimaging data analysis

Kong

Mizera

2016

Neurocomputing

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We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial quantile regression (PQR) basis for estimating functional coefficients. We further extend our partial quantile covariance techniques to functional composite quantile regression (CQR) defining partial composite quantile covariance. There are three major contributions. (1) We define partial quantile covariance between two scalar variables through linear quantile regression. We compute PQR basis by sequentially maximizing the partial quantile covariance between the response and projections of functional covariates. (2) In order to efficiently extract PQR basis, we develop a SIMPQR algorithm analogous to simple partial least squares (SIMPLS). (3) Under the homoscedasticity assumption, we extend our techniques to partial composite quantile covariance and use it to find the partial composite quantile regression (PCQR) basis. The SIMPQR algorithm is then modified to obtain the SIMPCQR algorithm. Two simulation studies show the superiority of our * Corresponding author Email address: lkong@ualberta.ca (Linglong Kong) 1 Part of the data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.ucla.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.ucla.edu/wp-content/ uploads/how to apply/ADNI Acknowledgement List.pdf proposed methods. Two real data from ADHD-200 sample and ADNI are analyzed using our proposed methods.

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“…The choice of 0 controls the optimal level of wavelet decomposition for the functional data. They improved wavelet-based LASSO by adding a prescreening step prior to the model fitting or, alternatively, by using a weighted version of wavelet-based LASSO [19]. Salama et al (2016) proposed a new LASSO algorithm, the minimum variance distortionless response (MVDR) LARS-LASSO [20], which solves the DOA problem in the CS framework.…”

Section: Introductionmentioning

confidence: 99%

“…By formulating the RBF neural network as a linear-in-theparameters model, they derived a 1 -constrained objective function for training the network. Zhao et al (2015) added two tuning parameters and 0 to the wavelet-based weighted-LASSO methods. The tuning parameter controls the model sparsity.…”

Section: Introductionmentioning

confidence: 99%

Method for Solving LASSO Problem Based on Multidimensional Weight

Chen

Lin

et al. 2017

Advances in Artificial Intelligence

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In the data mining, the analysis of high-dimensional data is a critical but thorny research topic. The LASSO (least absolute shrinkage and selection operator) algorithm avoids the limitations, which generally employ stepwise regression with information criteria to choose the optimal model, existing in traditional methods. The improved-LARS (Least Angle Regression) algorithm solves the LASSO effectively. This paper presents an improved-LARS algorithm, which is constructed on the basis of multidimensional weight and intends to solve the problems in LASSO. Specifically, in order to distinguish the impact of each variable in the regression, we have separately introduced part of principal component analysis (Part_PCA), Independent Weight evaluation, and CRITIC, into our proposal. We have explored that these methods supported by our proposal change the regression track by weighted every individual, to optimize the approach direction, as well as the approach variable selection. As a consequence, our proposed algorithm can yield better results in the promise direction. Furthermore, we have illustrated the excellent property of LARS algorithm based on multidimensional weight by the Pima Indians Diabetes. The experiment results show an attractive performance improvement resulting from the proposed method, compared with the improved-LARS, when they are subjected to the same threshold value.

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Wavelet-Based Weighted LASSO and Screening Approaches in Functional Linear Regression

Cited by 39 publications

References 36 publications

Wavelet-domain regression and predictive inference in psychiatric neuroimaging

Wavelet-domain regression and predictive inference in psychiatric neuroimaging

Partial functional linear quantile regression for neuroimaging data analysis

Method for Solving LASSO Problem Based on Multidimensional Weight

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