Sufficient Dimension Folding for Regression Mean Function

Xue, Yuan; Yin, Xiangrong

doi:10.1080/10618600.2013.859619

Cited by 22 publications

(17 citation statements)

References 33 publications

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“…[4] discussed matrix versions of principal component analysis and principal fitted components (PFC). [53] introduced central mean dimension folding subspace and proposed several methods to estimate it. [6] further developed tensor-valued sliced inverse regression.…”

Section: Review Of Methods For General Tensor-valued Datamentioning

confidence: 99%

Independent component analysis for tensor-valued data

Virta

Nordhausen

et al. 2017

Journal of Multivariate Analysis

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In preprocessing tensor-valued data, e.g. images and videos, a common procedure is to vectorize the observations and subject the resulting vectors to one of the many methods used for independent component analysis (ICA). However, the tensor structure of the original data is lost in the vectorization and, as a more suitable alternative, we propose the matrix- and tensor fourth order blind identification (MFOBI and TFOBI). In these tensorial extensions of the classic fourth order blind identification (FOBI) we assume a Kronecker structure for the mixing and perform FOBI simultaneously on each direction of the observed tensors. We discuss the theory and assumptions behind MFOBI and TFOBI and provide two different algorithms and related estimates of the unmixing matrices along with their asymptotic properties. Finally, simulations are used to compare the method's performance with that of classical FOBI for vectorized data and we end with a real data clustering example.Comment: 26 pages, 4 figure

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Section: Review Of Methods For General Tensor-valued Datamentioning

confidence: 99%

Independent component analysis for tensor-valued data

Virta

Nordhausen

et al. 2017

Journal of Multivariate Analysis

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“…Research dealing with high-dimensional matrix-valued variables (also known as matrix-variates) has attracted considerable attention in the past 10 years. There is a vast literature on dimension reduction techniques for matrix-variates (eg, Li et al, 2010;Ding and Cook, 2014;Xue and Yin, 2014;2015;Virta et al, 2017). In regression settings, existing methods for modeling matrix-variates as covariates focus on incorporating various regularization schemes that also preserve the inherent matrix nature of the covariate, for example, by imposing a low rank bilinear structure to the associated regression coefficients for the matrix-valued covariate (Hung and Wang, 2013;Zhou et al, 2013;Hoff, 2015;Jiang et al, 2017), applying a particular structured lasso penalty (Zhao and Leng, 2014), applying a nuclear norm penalty (Zhou and Li, 2014), and utilizing the envelope concept originally proposed in Cook et al (2010) to achieve supervised sufficient dimension reduction for tensor-variates (eg, Li and Zhang, 2017;Zhang and Li, 2017;Ding and Cook, 2018).…”

Section: Introductionmentioning

confidence: 99%

A Bayesian approach to joint modeling of matrix‐valued imaging data and treatment outcome with applications to depression studies

et al. 2019

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In this paper, we propose a unified Bayesian joint modeling framework for studying association between a binary treatment outcome and a baseline matrix‐valued predictor. Specifically, a joint modeling approach relating an outcome to a matrix‐valued predictor through a probabilistic formulation of multilinear principal component analysis is developed. This framework establishes a theoretical relationship between the outcome and the matrix‐valued predictor, although the predictor is not explicitly expressed in the model. Simulation studies are provided showing that the proposed method is superior or competitive to other methods, such as a two‐stage approach and a classical principal component regression in terms of both prediction accuracy and estimation of association; its advantage is most notable when the sample size is small and the dimensionality in the imaging covariate is large. Finally, our proposed joint modeling approach is shown to be a very promising tool in an application exploring the association between baseline electroencephalography data and a favorable response to treatment in a depression treatment study by achieving a substantial improvement in prediction accuracy in comparison to competing methods.

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“…For examples of particular dimension reduction methods incorporating matrix or tensor predictors, see e.g. [10], [11], [1] for independent component analysis, [12], [13], [14], [15] for sufficient dimension reduction and [16], [17] for principal components analysis-based techniques. More references are also given in [12], [1].…”

Section: Introductionmentioning

confidence: 99%

JADE for Tensor-Valued Observations

Virta

Nordhausen³

et al. 2018

Journal of Computational and Graphical Statistics

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Abstract-Independent component analysis is a standard tool in modern data analysis and numerous different techniques for applying it exist. The standard methods however quickly lose their effectiveness when the data are made up of structures of higher order than vectors, namely matrices or tensors (for example, images or videos), being unable to handle the high amounts of noise. Recently, an extension of the classic fourth order blind identification (FOBI) specifically suited for tensorvalued observations was proposed and showed to outperform its vector version for tensor data. In this paper we extend another popular independent component analysis method, the joint approximate diagonalization of eigen-matrices (JADE), for tensor observations. In addition to the theoretical background we also provide the asymptotic properties of the proposed estimator and use both simulations and real data to show its usefulness and superiority over its competitors.

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Sufficient Dimension Folding for Regression Mean Function

Cited by 22 publications

References 33 publications

Independent component analysis for tensor-valued data

Independent component analysis for tensor-valued data

A Bayesian approach to joint modeling of matrix‐valued imaging data and treatment outcome with applications to depression studies

JADE for Tensor-Valued Observations

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